Based on photogrammetric models of the first three Apollo landing sites, we have created a method to project virtual objects onto photos taken on the lunar surface. We have applied this method to search for stars in high-resolution scans of Apollo lunar photos and to restore views of the starry sky in some iconic images. Our method can be used to incorporate computer-generated 3D graphics, such as constellation boundaries, and coordinate and contour lines, into lunar images. This research has several applications, including the visualization of digital terrain models, the creation of a virtual planetarium based on lunar photos, and demonstration of object motion in lunar gravity for educational purposes.

The initial objective of this project was to identify stars in Apollo lunar photos from the Lunar and Planetary Institute (LPI). However, images taken by the Hasselblad Data Cameras (HDCs) do not typically feature easily distinguishable stars due to inadequate exposure and f-number settings, which were optimized for the lunar surface, space suits, and hardware. Celestial bodies visible in lunar photos are the Sun, Earth, and, in rare occasions, Venus (Lunsford & Jones, 2007). Small bright spots can also be observed in the sky in many images, although these may be film or scanning artifacts. Such artifacts can be identified as they appear randomly in multiple views taken almost simultaneously. Typically, they exhibit irregular shapes and acquire color when only the upper emulsion layer is affected or damaged. Often, similar artifacts can be observed not only in the sky but also in other dark areas of the image, as shown in Figure 1. The possibility of detecting real stars and planets in these images remained uncertain.
Figure 1.

Apollo 11 mission photos AS11-40-5874 (a) and AS11-40-5875 (b) from LPI captured with a very short time interval between shots. Bright spots in the sky are highlighted with white circles. In image (a), similar spots within the shadow of the Lunar Module are also encircled. The non-coinciding positions of the spots in the sky between the two images suggest that they are image artifacts rather than stars.

Figure 1.

Apollo 11 mission photos AS11-40-5874 (a) and AS11-40-5875 (b) from LPI captured with a very short time interval between shots. Bright spots in the sky are highlighted with white circles. In image (a), similar spots within the shadow of the Lunar Module are also encircled. The non-coinciding positions of the spots in the sky between the two images suggest that they are image artifacts rather than stars.

Close modal

In recent years, we have developed 3D models of the first three Apollo landing sites using an extensive photogrammetric analysis of numerous photos (Pustynski & Jones, 2014; Pustynski, 2022, 2021a, 2021b; Pugal & Pustynski, 2022). Our high-precision models include camera coordinates and rotations. Using these data, we developed an algorithm and computer code to calculate positions of stars and planets in Apollo photos. Although we were unable to detect even the brightest stars such as Canopus due to inadequate exposure settings, we successfully recreated views of the starry sky and constellations in some iconic lunar images. Our algorithm has potential for a wide range of applications. By inserting virtual objects into the 3D space of the landing sites, it is possible to create augmented reality based on the lunar environment. These visualizations may be used for scientific and educational purposes. In addition to drawing constellations and coordinate grids, we generated terrain modeling contour lines and demonstrated a realistic visualization of free fall under lunar gravity.

A detailed description of the process for creating a photogrammetric model of an Apollo landing site can be found in Pustynski and Jones (2014) and Pustynski (2021a). The resulting model includes coordinates and rotations of camera stations. However, since lunar photos do not contain explicit references to the local horizontal plane and cardinal points, the initial coordinate frame of the model is arbitrary and linked to hardware elements or adjacent rocks. In our first Apollo 11 landing site model (Pustynski & Jones, 2014), an approximate method was used to determine the local horizontal frame, which assumed the Solar Wind Composition Experiment (SWC) pole to be vertical and cardinal directions to be set according to orbital photos. However, this method does not provide the required accuracy for our purpose.

To introduce the horizontal coordinate frame for the Apollo 11 and Apollo 14 landing site models, we developed a new much more accurate method that involves aligning the coordinate axes with two or more celestial bodies present in the images. The essence of this method is as follows. The unit vectors pointing to these bodies (C1; and C2; in Figure 2, though there may be more) are known in the horizontal frame of the landing site because time instances at which the photos were taken can be determined with great accuracy from voice transcripts and other data sources (Jones & Glover, 2018). We used Jet Propulsion Laboratory Solar Systep Dynamics Group's Horizons (JPL SSD Group, 2023) to obtain the horizontal coordinates of the celestial bodies. These directions can also be determined in the initial coordinate frame of the model (vectors C1mod and C2mod in Figure 2; the axes of the model coordinate frame are not shown to avoid cluttering the figure). Next, average directions Cavg, Cavgmod of the vector pairs (C1;,C2;) and (C1mod,C2mod) are calculated. Initially, the directions Cavg and Cavgmod are different, with the angle between them denoted by θ (Figure 2a). To align the coordinates, we perform two rotations of the model coordinate frame. In the first step, the model coordinate frame is rotated by the angle θ until the directions Cavg and Cavgmod coincide (Figure 2b). In the final step, the model coordinate frame is rotated about the vector Cavg by an angle α that minimizes the value of S given by Equation 1:
S=1Ni=0NΔαi2,
(1)
where N is the total number of celestial bodies used and Δαi is the angle between the actual direction of celestial body number i and its direction in the model (Figure 2c).
Figure 2.

Aligning the model coordinate frame with the local horizontal frame.

Figure 2.

Aligning the model coordinate frame with the local horizontal frame.

Close modal

Our method ensures that the transformed coordinates of the celestial bodies in the model closely match their actual horizontal coordinates, resulting in a transformed coordinate frame that closely approximates the true horizontal frame. We achieved high accuracy for the Apollo 11 and Apollo 14 missions, with S values in Equation 1 approximately equal to 0.1° and 0.2°, respectively.

The Sun can be used in all models, despite its center being difficult to determine due to glare. However, its direction can be deduced by analyzing the shadows cast by tall pointed objects such as the flagpole or the SWC pole (Pustynski, 2021a). Earth is present in photos from the Apollo 11 and Apollo 14 missions, and its center can be easily identified as the center of the circumscribed circle. For the Apollo 14 mission, we also used Venus as a third celestial body. Unfortunately, Apollo 12 photos allowed only for the use of the Sun. In this case, we used a modified version of our algorithm. The mean plane of rocks scattered at different distances from the Lunar Module (LM) was identified with the local horizontal plane. While this approach may have resulted in slightly larger deviations of the transformed coordinates from the true horizontal frame, the error is still sufficiently small (Pustynski, 2021a).

2.1 Checking Accuracy of the Transformed Coordinate Frame

Since the precise determination of camera orientation is crucial to our study, we conducted independent checks to validate the model coordinate frame.

2.1.1 Tilt of the Lunar Module

The tilt of the LM on the lunar surface is well-known from the navigation data (Orloff, 2004), and can also be found photogrammetrically. The vertical axis of the LM was determined by identifying the normal to the plane of the fittings at the top of the primary struts, as shown in Figure 3. Our analysis yielded a tilt angle of 4.65° for Apollo 11, which closely matches the value derived from navigation data (4.5°). Similar results were obtained for the LM of Apollo 12 and the Surveyor 3 probe at the Apollo 12 landing site (Pustynski, 2021a), as well as for the LM of Apollo 14.
Figure 3.

Tilt of the LM in the photo AS11-40-5848. The fittings +Z, -Z, and -Y are located at the top of the primary struts (the +Y fitting is behind the LM), and the LM axis is perpendicular to the plane of these fittings. The angle α represents the tilt of the LM with respect to the local vertical. The long horizontal line represents the astronomical horizon, with the point on this line indicating the north. To remove the tilt of the astronomical horizon, the image has been rotated.

Figure 3.

Tilt of the LM in the photo AS11-40-5848. The fittings +Z, -Z, and -Y are located at the top of the primary struts (the +Y fitting is behind the LM), and the LM axis is perpendicular to the plane of these fittings. The angle α represents the tilt of the LM with respect to the local vertical. The long horizontal line represents the astronomical horizon, with the point on this line indicating the north. To remove the tilt of the astronomical horizon, the image has been rotated.

Close modal

2.1.2 Large-Scale Tilt of the Landing Site

The Apollo 11 landing site has a northeast tilt of several tenths of degree at a scale of several kilometers. This tilt can be deduced from Digital Terrain Models (DTM) based on orbital photos (Arizona State University, 2012). We discovered a similar tilt in the photogrammetric model by analyzing the distribution of rocks around the LM. The mean plane of 28 rocks scattered at distances from tens to hundreds of meters around the LM was found to have a tilt of approximately 1.1° with an azimuth of about 70° from north. This value falls within the expected accuracy margin.

2.1.3 Elevation of Distant Objects

In Apollo 11 photos taken in the northwestern direction across a vast plain, some objects at a distance of several kilometers can be seen. We identified a unique feature (two adjacent dark spots resembling portions of a crater rim) in a number of photos (see crops in Figures 4a, 4b, and 4c). According to the model, the feature is approximately 3.6±0.3 km from the LM at the azimuth of 12.3°. Generally, the range uncertainty for objects at this distance is much larger. Fortunately, in this case, the uncertainty is smaller because the parallax of the camera stations from which the object was detected exceeds 70 m (see Figure 4d). The only object that can be spotted in the map (Applied Coherent Technology, 2023) within the corresponding range of azimuths and distances is a fresh 135-m crater situated at the rim of a much larger crater (see Figure 4e). The elevated rim of the larger crater facilitates visibility of the 135-m crater, which remains the farthest object we were able to identify in the Apollo 11 photos. The negative elevation of the feature in the transformed coordinates is -35 m. According to the elevation map (Arizona State University, 2012), the LM negative elevation is in the range of -1930 to -1920 m, while the 135-m crater's elevation range is -1960 to -1950 m. Thus, the crater lies approximately 30±10 m below the LM. The precision with which the elevation difference is measured confirms the accuracy of the transformed coordinates, as an error of 0.5° in the determination of the horizontal plane would result in an elevation error of 3400×sin0.530 m.
Figure 4.

The rim of a distant 135-m crater is highlighted in elliptical insets in the photos AS11-40-5868 (a), AS11-40-5885 (b), and AS11-40-5958 (c). The square inset represents a rock located approximately 100 meters to the north from the LM, providing a reference point. In (d), the camera stations of the photos (a)–(c), as well as the LM, Laser Ranging Retroreflector (LRRR), Passive Seismic Experiment Package (PSEP), Little West Crater, and Double Crater are labeled in the Lunar Reconnaissance Orbiter image M131494509L (LROC Apollo 11, n.d.). The angle θ represents the angular distance between the southern azimuth and the direction towards the LRRR, as measured from the LM. In (e), this crater is encircled; two straight lines point from the LM to azimuths 12.3±0.5 deg; the brighter portions of the lines label the distance uncertainty range. The center of the crater is situated 3.4 km from the LM.

Figure 4.

The rim of a distant 135-m crater is highlighted in elliptical insets in the photos AS11-40-5868 (a), AS11-40-5885 (b), and AS11-40-5958 (c). The square inset represents a rock located approximately 100 meters to the north from the LM, providing a reference point. In (d), the camera stations of the photos (a)–(c), as well as the LM, Laser Ranging Retroreflector (LRRR), Passive Seismic Experiment Package (PSEP), Little West Crater, and Double Crater are labeled in the Lunar Reconnaissance Orbiter image M131494509L (LROC Apollo 11, n.d.). The angle θ represents the angular distance between the southern azimuth and the direction towards the LRRR, as measured from the LM. In (e), this crater is encircled; two straight lines point from the LM to azimuths 12.3±0.5 deg; the brighter portions of the lines label the distance uncertainty range. The center of the crater is situated 3.4 km from the LM.

Close modal

2.1.4 Azimuth of the Laser Ranging Retroreflector (LRRR) Station

The azimuth of the LRRR station relative to the center of the LM can be independently determined from DTMs (Wagner et al., 2017), as shown in Figure 4d. The same azimuth measured in the transformed coordinates differs from the DTM-based value by less than 0.2°. This confirms that the transformed coordinates are accurately aligned with the cardinal directions.

2.1.5 Conclusion

The arbitrary initial coordinate frame of the model can be accurately transformed to the horizontal frame. The resulting frame differs from the true horizontal frame by less than 0.3° or so. After the coordinate transformations, camera orientation at each station is represented by three angles: azimuth ϕ (measured clockwise from north), elevation θ (measured from the nadir), and roll ψ (measured clockwise with the astronomical horizon parallel to the lower edge of the frame when ψ=0); see Figure 5 for reference. Although camera coordinates are not required to project stars onto the image plane (since celestial bodies are infinitely far away), they are needed to augment photos with closer virtual objects. The transformed coordinate frame axes x, y, and z correspond to east, north, and zenith, respectively.
Figure 5.

Camera rotations. The arrows indicate the positive directions of the rotations. (a) Azimuth ϕ represents the rotation of the camera about the local vertical axis. It is measured clockwise from north. (b) Elevation θ denotes the angle between the nadir direction and the optical axis of the camera. (c) Roll ψ refers to the rotation about the optical axis. The figure provides a schematic view from the back of the camera.

Figure 5.

Camera rotations. The arrows indicate the positive directions of the rotations. (a) Azimuth ϕ represents the rotation of the camera about the local vertical axis. It is measured clockwise from north. (b) Elevation θ denotes the angle between the nadir direction and the optical axis of the camera. (c) Roll ψ refers to the rotation about the optical axis. The figure provides a schematic view from the back of the camera.

Close modal

Our next task is to project a distant point-like object with the known altitude α and azimuth γ onto the image plane of a specific photograph. We assume that the HDC lens is free of distortions, which is a reasonable first-order assumption based on the parameters of the Zeiss Biogon lens (see Carl Zeiss, n.d.). We utilized the same assumption when constructing our models of the landing sites.

In the first step, we calculate the unit direction vector of the camera's optical axis:
c^=sinθsinϕ,sinθcosϕ,-cosθ.
Next, we calculate the auxiliary vector h; (see Figure 6):
h;=k^×c^,
where k^=(0,0,1) is the unit vector of the z-axis, and the corresponding unit vector is h^. The unit vector h^ lies in the image plane (as it is perpendicular to the optical axis) and is parallel to the astronomical horizon (as it is perpendicular to the z-axis). If the camera roll is zero (ψ=0), this vector is parallel to the lower edge of the frame and points to the left.
Figure 6.

Projecting a point in the direction o^ to the image plane. The black dot in the center of the plane is the principal point. ximage and yimage are coordinate axes of the image frame; their direction is the same as used in computer graphics.

Figure 6.

Projecting a point in the direction o^ to the image plane. The black dot in the center of the plane is the principal point. ximage and yimage are coordinate axes of the image frame; their direction is the same as used in computer graphics.

Close modal
In the second step, we calculate the unit direction vector of the point to be projected:
o^=cosαsinγ,cosαcosγ,sinα.
Next, we introduce two auxiliary unit vectors p^ and op^:
px=o^×c^,op^=c^×p^.
Both vectors lie in the image plane since they are perpendicular to c^. Since p^o^ and op^p^, the unit vector op^ is the orthogonal projection of the vector o^ onto the image plane. Therefore, the object's image is projected on the direction of the vector op^.
The distance dR (in millimeters) of the object's projection R from the principal point depends on the angle γ=arccos(c^·o^) between the direction to the object and the optical axis. Specifically, we have
dR=Ftanγ,
where F is the principal distance in millimeters. The principal distance is determined by the focal distance f of the lens (61.1 mm for Zeiss Biogon) and the distance d to which the camera is focused:
1F=1f-1d.
The focusing distance should be estimated individually for each photograph by observing objects blurring, as described in detail in Pustynski (2021a). Objects with γ<90 are located in front of the image plane and can appear in photographs when γ is smaller than half the camera's field of view (approximately 50° for HDC cameras). However, larger values of γ can be used for graphical representation of objects outside the photo frame.
Once we have determined the projection point R, we can find its linear coordinates in the image plane. The angle between the unit vectors h^ and op^ is given by δ=±arccos(h^·op^). To determine the correct sign of δ, we calculate the scalar parameter n=c^·h^×op^. This triple product can be thought of as follows: the vector h^×op^ is parallel or antiparallel with c^, depending on whether op^ is above or below the line of h^. Therefore, the sign of the scalar product c^·h^×op^ is positive if op^ is above this line, and negative if it is below. The sign function then takes care of the rest, yielding:
δ= sgn (n) arccos (h^·op^).
In Figure 6, δ is negative, so we show the equivalent angle 360+δ instead.
The camera roll ψ is then considered as follows:
δ'=δ-ψ.
The linear coordinates (ximage,yimage) of point R in the image plane can be calculated:
ximage=x0-dRcosδ',yimage=y0-dRsinδ',
where (x0,y0) are the coordinates of the principal point, which is the center of the central réseau cross.

When analyzing digital scans, it is necessary to multiply the linear coordinates (ximage,yimage) by the pixel-to-millimeter scale of the scan. This scale can be determined by using the réseau grid again (the distance between two adjacent crosses is 10 mm in the film). It is important to measure this scale for each photograph individually, as it can vary from scan to scan.

There are several factors to consider when working with film scans. Firstly, it is important to note that the horizontal and vertical pixel scales of the available scans may differ slightly. However, we found that this difference is small enough to use the average scale. Secondly, some scans may be slightly rotated, meaning that the entire réseau is rotated by a small amount. This rotation should be taken into account when the angle δ' is calculated. In the Apollo 11 landing site model, the camera roll was measured from the middle horizontal line of the crosses, and the rotation of the scan was added as correction to the camera roll. For the Apollo 12 and Apollo 14 models, the roll is measured from the horizontal line of scans downloaded from the Lunar and Planetary Institute website (Lunar and Planetary Institute, n.d.), so no additional correction was needed. However, scans from a different source may require roll correction. Thirdly, other deformations of the scanned film (revealed as varying distances between réseau crosses) are small enough to be ignored. Finally, it is problematic to work with photos taken from the LM windows with the Hasselblad Electric Camera (HEC), as it lacked the réseau plate. In these scans, principal point coordinates, scale, and roll of the scan can only be estimated roughly, so we prefer not to use HEC photos.

We developed a computer code that calculates coordinates of 3D point projections onto the image plane of photos taken from different camera stations. The code also draws these projections graphically and performs other tasks (Pustynski, 2023). The produced digital images are provided with a réseau grid to match them to scans of original photographs. We used the Asymptote Vector Graphic Language1 to write the code. In the following sections, we present several combined images.

3.1 Checking the Algorithm

We have carried out multiple checks of our algorithm and code. First of all, we used model benchmarks (rocks and elements of hardware) as test objects. The direction vector of such a benchmark for the specific camera is oc=B;-C;, where B;=(xB,yB,zB) is the benchmark position vector and C;=(xC,yC,zC) is the camera position vector. We calculated pixel coordinates of a number of benchmarks in different scans and found a very good agreement between the calculated coordinates and actual images of benchmark objects.

With our algorithm, we can create virtual objects in the 3D space of the landing site's surroundings by predefining coordinates of points in this space. Views of such an object can be generated and added to photographs taken from different camera stations. In a photogrammetric software package, this virtual object should be indistinguishable from real objects, as it obeys the same rules of perspective. Lines of sight from different cameras should intersect at points on the object, and coordinates of these points can be determined with the instruments provided by the package. To verify our algorithm, we created virtual objects in the 3D space and determined coordinates of their points with ImageModeler 2009 (the software used to compile the photogrammetric models).

As an example, Figure 7 shows crops of four photos from the Apollo 11 landing site with a virtual cube inserted into the 3D space. The lines of sight from the four camera stations converge at one of the vertices of the cube, and two ImageModeler rulers measuring the edges of the cube are also shown. The measured edge lengths differ by less than 2 cm from the predefined length. Additionally, we determined the coordinates of three vertices labelled with benchmarks (small crosses). Their displacements from the predetermined locations range from 1.7 cm to 2.2 cm, which can be attributed to small errors in determination of camera coordinates and rotations. These values are consistent with the accuracy estimations of the photogrammetric models; see Pustynski and Jones (2014) and Pustynski (2021a) for details. We assumed a Lambertian reflectance for the faces of the cube, and the shadow was generated based on the terrain model of Double Crater (see Section 7). The position and shape of the shadow depend on solar coordinates. Full-size color versions of the individual images in Figure 7 can be found in Pustynski (2023).
Figure 7.

Crops from photos AS11-39-5764 (a), AS11-40-5852 (b), AS11-40-5889 (c), and AS11-40-5941 (d) with a 1.5×1.5×1.5 m virtual cube inserted into 3D space of the Tranquility Base. Lines of sight from the four camera stations converge at one of the vertices. Two edge lengths are measured by perpendicular rulers. Tiny squares and circles are calibration benchmarks scattered over the scene.

Figure 7.

Crops from photos AS11-39-5764 (a), AS11-40-5852 (b), AS11-40-5889 (c), and AS11-40-5941 (d) with a 1.5×1.5×1.5 m virtual cube inserted into 3D space of the Tranquility Base. Lines of sight from the four camera stations converge at one of the vertices. Two edge lengths are measured by perpendicular rulers. Tiny squares and circles are calibration benchmarks scattered over the scene.

Close modal

Based on these results, we conclude that our projecting algorithm is functioning properly.

To find a celestial body position in a lunar photograph, its horizontal coordinates at the time of shooting are needed. Fortunately, the shooting times of many lunar photographs can be determined with an accuracy of about 1 min from voice transcripts and TV recordings (Jones & Glover, 2018). The celestial bodies' horizontal coordinates depend on the selenographic coordinates of the landing site. JPL Horizons (JPL SSD Group, 2023) is a tool providing horizontal coordinates of the solar system bodies at any point on the lunar surface, including the Apollo landing sites, at any time during the Apollo expeditions. We use solar and planetary ephemerides from this source to accurately calculate the positions of celestial bodies. Additionally, we use distances to the Sun and Earth to reproduce their angular sizes correctly. However, JPL Horizons does not provide horizontal coordinates of objects outside the solar system. To find the horizontal coordinates of stars, we transform their equatorial coordinates using two solar system bodies as references. The Sun and any planet, or any pair of planets, can be used as references to perform this transformation.

Figure 8 illustrates our method. B1 and B2 represent two reference celestial bodies with known equatorial and horizontal coordinates, allowing us to calculate their unit directional vectors B1e; and B2e; in the equatorial frame. Similarly, their unit vectors B1h;; and B2h;; in the horizontal frame can be calculated based on their known horizontal coordinates (the upper indices e and h are omitted in Figure 8 as they represent the same vectors B1; and B2; in different frames). The star O has known equatorial coordinates, allowing us to calculate its unit directional vector Oe; in the equatorial frame. However, we need to determine its horizontal coordinates. To achieve this, we introduce two auxiliary vectors, BB; and BO;, in the equatorial frame, along with two angles α and β:
BBe;=B2e;×B1e;,BOe;=B2e;×Oe;,α=karccos(BBe;·BOe;),β=arccos(B2e;·Oe;).
Here k=±1; the choice of the sign is explained below. It is seen that α is the angle between BB; and BO; and β is the angle between B2; and O;. We also find the vector BB; in the horizontal frame: BBh;;=B2h;;×B1h;;.
Figure 8.

Finding horizontal coordinates of a star O from its equatorial coordinates. B1 and B2 are two benchmark objects with known equatorial and horizontal coordinates.

Figure 8.

Finding horizontal coordinates of a star O from its equatorial coordinates. B1 and B2 are two benchmark objects with known equatorial and horizontal coordinates.

Close modal

Now we proceed with two rotations: (1) The vector BBh;; is rotated by an angle α around the vector B2h;; in the direction depicted in Figure 8. This rotation takes place in the horizontal frame. The resulting vector aligns with BO;, allowing us to deduce the horizontal coordinates of BOh;;. It is not possible to determine them directly from the cross product of vectors B2; and O; since initially the horizontal coordinates of O; are unknown. (2) Finally, the vector B2h;; is rotated by the angle β around the vector BOh;; (obtained after the first rotation). This rotation occurs in the direction indicated in Figure 8, and the resulting vector aligns with O;. As these rotations are performed within the horizontal frame, we obtain the horizontal coordinates of the object Oh;; after the second rotation.

It is important to note that the direction of the first rotation depends on whether the object is located above or below the plane defined by the reference objects' vectors (as in Figure 8). To ensure the correct direction, we multiply α by the parameter k= sgn (B2;·[ BB ;× BO ;]). If the object is above the plane, the cross product in the brackets is parallel to B2;, the dot product is positive, and the rotation by the angle α is performed clockwise. If the object is below the plane, the dot product is negative, and the rotation is performed counterclockwise.

To find horizontal coordinates of stars at any photograph, we use ephemerides of the Sun and planets calculated with JPL Horizons and tabulated at 1-min intervals. Two reference objects are needed. Theoretically, higher accuracy is provided when the angle B1B2 is close to ±90°, but practically, the error is very small even when this angle is much larger or smaller.

4.1 Accuracy Verification

To validate the accuracy of our coordinate transformation, we used the digital planetarium software Stellarium2 to calculate the horizontal coordinates of some stars at the landing sites. We found that the discrepancies between the coordinates provided by Stellarium and those calculated through our transformation were less than one minute of arc, which is significantly smaller than the model's uncertainty. Any discrepancies observed can likely be attributed to differences in the algorithms used by JPL Horizons and Stellarium.

To verify the accuracy of our method, we compared the predicted positions of Earth and Venus with their actual locations in lunar photographs. Figures 9a and 9b show the calculated positions and sizes of Earth superimposed onto two photographs from the Apollo 11 and Apollo 14 missions. The linear offset between the predicted and actual locations of Earth is around 0.1–0.15 mm, which corresponds to an angular offset in the range of 0.11–0.16° (assuming that 1 mm in the film corresponds to approximately 0.9° of the field of view). This offset is consistent with our estimate of the camera rotations uncertainty, which is approximately 0.3°. In 3900×3900 px crops from LPI, a 0.15 mm offset corresponds to 11 pixels.
Figure 9.

Calculated position and size of Earth (represented by a circle) in the photos AS11-40-5929 (a) and AS14-64-9189 (b). The linear distance between the tick marks is 1.0 mm in the original film. In (c), actual positions of Venus (indicated by stars) in the photographs from AS14-64-9189 to AS14-64-9197 are presented relative to its calculated location (the center of the target). The radii of the target circles are 0.2 mm and 0.4 mm in the original film. Camera roll rotations are compensated to zero.

Figure 9.

Calculated position and size of Earth (represented by a circle) in the photos AS11-40-5929 (a) and AS14-64-9189 (b). The linear distance between the tick marks is 1.0 mm in the original film. In (c), actual positions of Venus (indicated by stars) in the photographs from AS14-64-9189 to AS14-64-9197 are presented relative to its calculated location (the center of the target). The radii of the target circles are 0.2 mm and 0.4 mm in the original film. Camera roll rotations are compensated to zero.

Close modal

In Figure 9c, we have marked the actual locations of Venus in 9 photographs from the Apollo 14 mission using small stars. Venus is depicted relative to its predicted location (the center of the target). For the compilation of Figure 9c, we intentionally adjusted the horizontal frame in the Apollo 14 landing site model. While our basic horizontal frame is aligned using the Sun, Earth, and Venus as described in Section 2, for Figure 9c, we aligned the horizontal frame using only the Sun and Earth. By doing so, the coordinate system becomes independent of Venus, allowing the deviation of the actual locations of Venus from its predicted position in this figure to better represent the deviation we may expect for an arbitrary star. The average distance between the actual and predicted locations is approximately 0.27 mm (equivalent to 0.25°), which can be attributed to the uncertainty of the coordinate frame. The dispersion of the actual locations is primarily caused by the uncertainty in the orientations of individual camera stations within the model.

Although a huge glare makes the solar disk invisible in Apollo photographs, we used lens flare for an indirect accuracy check. In Figure 10, the solar disk is drawn at its calculated position in the photograph AS12-46-6767, and a straight line is drawn through the central cross along the symmetry axis of the “bubbles.” The solar disk is expected to be situated at this line, but a small displacement is present. The angular displacement is 0.3–0.4°. Although this method is not very accurate (and the Apollo 12 model coordinates alignment may be less accurate as well; see Section 2), this value is also in good agreement with the expected accuracy of the model.
Figure 10.

Lens flare and calculated positions of the Sun (the dark circle) in the photograph AS12-46-6767. A straight line is drawn through the central cross along the symmetry axis of the “bubbles.” The image is darkened to reveal more details of the flare.

Figure 10.

Lens flare and calculated positions of the Sun (the dark circle) in the photograph AS12-46-6767. A straight line is drawn through the central cross along the symmetry axis of the “bubbles.” The image is darkened to reveal more details of the flare.

Close modal
In Figure 11, the restored starry sky view of Apollo 11 mission photo AS11-40-5869 is compared to the modeled view of approximately the same sky region generated by Stellarium. The Stellarium view was produced for the Apollo 11 landing site coordinates on the 21st of July, 1969, at 3:13 GMT, which corresponds to the time when the photo was taken according to Jones and Glover (2018). The positions of stars in both images exhibit a high degree of similarity, indicating the accuracy of our model. It is worth noting that Kochab, with its azimuth/elevation of 1558'12''/-036'19'' according to our model and 1558'08''/-036'53'' according to Stellarium, was technically visible to the astronauts due to the depression of the terrain, even though it was below the astronomical horizon at that moment. For more detailed information on the modeling of the starry sky, refer to Section 6.
Figure 11.

Comparison of the modeled starry sky in the Apollo 11 mission photo AS11-40-5869 (a) and an image of approximately the same region according to Stellarium (b). The mission photo was rotated to eliminate the tilt of the astronomical horizon, which is depicted by the white horizontal line. The direction to the north is indicated by the letter N. The size of each grid cell in (b) is 5×5°. The boundaries of the region in (a) and (b) are slightly different due to the use of different projections.

Figure 11.

Comparison of the modeled starry sky in the Apollo 11 mission photo AS11-40-5869 (a) and an image of approximately the same region according to Stellarium (b). The mission photo was rotated to eliminate the tilt of the astronomical horizon, which is depicted by the white horizontal line. The direction to the north is indicated by the letter N. The size of each grid cell in (b) is 5×5°. The boundaries of the region in (a) and (b) are slightly different due to the use of different projections.

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Based on our analysis, we can conclude that the error in the calculated coordinates of objects in the image plane is reasonably small. This level of accuracy enables us to effectively search for stars in Apollo photographs. The precision of the calculated coordinates provides confidence in the reliability of our method for identifying celestial objects in the images.

Due to the astronauts' primary focus on capturing images of the lunar surface and expedition-related equipment, only a small portion of the lunar sky is visible in Apollo photographs. Typically, the visible lunar horizon divides a photograph into two parts, with the sky occupying the upper half or even less of the image. With the 52-mm linear size of the frame edge and the camera focal length of 61.1 mm, the angular half-size of the image covers only arctan522·61.123°, which corresponds to a strip 20% of the celestial sphere. Consequently, many bright celestial bodies did not appear in the photographs, either due to their position below or too high above the horizon. It is not surprising, therefore, that Sirius, the brightest star aside from the Sun, was not inside the frame of any of the 123 photographs taken by the Apollo 11 crew during their extravehicular activity (EVA). Unfortunately, Sirius was also not inside the frame of the nearly 300 of Apollo 12 photographs included in the model (Pustynski, 2021b), or in the 65 of Apollo 14 photographs in the model (Pugal & Pustynski, 2022). Venus appeared in nine Apollo 14 EVA photographs taken by Alan Sheppard, who raised his camera to capture images of Earth and Venus high above the LM. Mercury, being very close to the Sun, was always hidden in the solar glare, while other bright planets were simply outside the frame of the photographs.

The second brightest star, Canopus or α Carinae, had the potential to appear in some of the Apollo 11 and Apollo 12 photographs thanks to its apparent magnitude of approximately -0.7m. However, compared to Venus, which had an apparent magnitude of -4.4m during the Apollo 14 mission (JPL SSD group, 2023), Canopus was approximately 30 times dimmer. This difference is substantial. Nevertheless, Venus is distinguishable both in black-and-white and color photographs, as seen in Figure 12. The black-and-white photographs appear clearer, possibly because of their higher dynamic range and increased linear resolution in comparison to the color film. As a result, we were cautiously optimistic about our prospects of locating Canopus in some EVA photographs.
Figure 12.

Venus in Apollo 14 photographs (cropped, enlarged, and enhanced). (a) and (b): black-and-white photographs AS14-64-9190 and AS14-64-9191 taken during the 2nd EVA. (c) and (d): color photographs AS14-66-9226 and AS14-66-9227 taken from orbit. Venus has a linear size of 0.05–0.08 mm in these crops, mostly due to diffraction and blurring.

Figure 12.

Venus in Apollo 14 photographs (cropped, enlarged, and enhanced). (a) and (b): black-and-white photographs AS14-64-9190 and AS14-64-9191 taken during the 2nd EVA. (c) and (d): color photographs AS14-66-9226 and AS14-66-9227 taken from orbit. Venus has a linear size of 0.05–0.08 mm in these crops, mostly due to diffraction and blurring.

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5.1 Searching for Canopus

Canopus was the most obvious star to search for in the lunar photographs. Other bright stars, such as α Centauri, Arcturus, and Vega, are 1.5–2 times dimmer. We began by examining all the Apollo 11 photographs that could potentially include Canopus, as listed in Table 1. The predicted coordinates of Canopus are given relative to the principal point of the photograph, which is the center of the central cross. We excluded photos taken from the 4 o'clock panorama station, as Canopus was hidden behind the LM. In the lower portion of the table, we added some, but not all, Apollo 12 expedition photographs that could potentially feature Canopus.

Table 1.

Apollo 11 and Apollo 12 Photographs That May Potentially Feature Canopus

Photo indexTime (UTC)Az (°)El (°)X (mm)Y (mm)Comment
AS11-40-5851 Jul 21, 3:04 166.33 6.96 17.73 12.36 Ladder panorama 
AS11-40-5859 Jul 21, 3:06 166.34 6.97 -2.21 25.35 View towards the ladder 
AS11-40-5860 Jul 21, 3:06 166.34 6.97 11.63 24.16 View towards the ladder 
AS11-40-5861 Jul 21, 3:06 166.34 6.97 -17.85 19.67 View towards the ladder 
AS11-40-5874 Jul 21, 3:43 166.38 7.05 -6.69 12.91 Aldrin and the flag 
AS11-40-5875 Jul 21, 3:43 166.38 7.05 -6.27 13.20 Aldrin and the flag 
AS11-40-5889 Jul 21, 4:05 166.41 7.09 12.67 20.65 12 o'clock panorama 
AS11-40-5890 Jul 21, 4:05 166.41 7.09 -20.56 23.71 12 o'clock panorama 
AS11-40-5938 Jul 21, 4:29 166.44 7.14 -2.29 18.45 8 o'clock panorama 
AS11-40-5944 Jul 21, 4:30 166.44 7.15 -23.76 18.79 Aldrin moving to the EASEP site 
AS12-47-6945 Nov 19, 14:51 192.83 11.97 -1.97 14.76 Bean's 12 o'clock panorama 
AS12-47-6966 Nov 19, 14:54 192.83 11.96 10.49 11.78 Bean's 8 o'clock panorama 
AS12-48-7042 Nov 20, 4:30 193.87 10.24 -22.08 22.19 Solar Wind Composition; B&W 
AS12-48-7140 Nov 20, 7:02 194.04 9.90 -10.05 10.49 Block Crater panorama; B&W 
Photo indexTime (UTC)Az (°)El (°)X (mm)Y (mm)Comment
AS11-40-5851 Jul 21, 3:04 166.33 6.96 17.73 12.36 Ladder panorama 
AS11-40-5859 Jul 21, 3:06 166.34 6.97 -2.21 25.35 View towards the ladder 
AS11-40-5860 Jul 21, 3:06 166.34 6.97 11.63 24.16 View towards the ladder 
AS11-40-5861 Jul 21, 3:06 166.34 6.97 -17.85 19.67 View towards the ladder 
AS11-40-5874 Jul 21, 3:43 166.38 7.05 -6.69 12.91 Aldrin and the flag 
AS11-40-5875 Jul 21, 3:43 166.38 7.05 -6.27 13.20 Aldrin and the flag 
AS11-40-5889 Jul 21, 4:05 166.41 7.09 12.67 20.65 12 o'clock panorama 
AS11-40-5890 Jul 21, 4:05 166.41 7.09 -20.56 23.71 12 o'clock panorama 
AS11-40-5938 Jul 21, 4:29 166.44 7.14 -2.29 18.45 8 o'clock panorama 
AS11-40-5944 Jul 21, 4:30 166.44 7.15 -23.76 18.79 Aldrin moving to the EASEP site 
AS12-47-6945 Nov 19, 14:51 192.83 11.97 -1.97 14.76 Bean's 12 o'clock panorama 
AS12-47-6966 Nov 19, 14:54 192.83 11.96 10.49 11.78 Bean's 8 o'clock panorama 
AS12-48-7042 Nov 20, 4:30 193.87 10.24 -22.08 22.19 Solar Wind Composition; B&W 
AS12-48-7140 Nov 20, 7:02 194.04 9.90 -10.05 10.49 Block Crater panorama; B&W 

NOTE. Time instants the photographs were taken (according to Jones & Glover, 2018) are in the second column. (Az, El) are the horizontal coordinates of Canopus. (X, Y) are linear coordinates in the image plane, the origin is in the center of the big réseau cross, the x-axis is parallel to the middle line of crosses, and the y-axis is pointed upwards.

The accuracy of coordinates in Table 1 can be estimated based on the uncertainty of the model, which is about 0.3° or better. The linear uncertainty of the coordinates is approximately 61.1·tan0.30.3 mm near the center of the image and slightly larger near the edge. A conservative value ΔX=ΔY=0.4 mm may be adopted, which is approximately 0.8% of the edge length (see for comparison Figure 9c), where the distance between the actual and predicted location of Venus never exceeds 0.4 mm). For the 3900×3900 px scans from LPI, this is equivalent to 30 px. However, we believe that the actual error is smaller in most cases. The uncertainty of the shooting time is negligible because the horizontal coordinates of stars change at a maximum rate of 0.5°/h, so a timing error of 5 min results in a coordinate error less than 0.05°.

We tried to spot Canopus in Apollo 11 high-resolution RAW scans (resolution 200 px/mm, 14-bit A/D) (NASA/JSC/ASU) at coordinates provided in Table 1. Unfortunately, our efforts failed. In Figure 13, the expected locations of Canopus in four photographs are depicted with white dots. The insets in the figure show enlarged and enhanced views of the corresponding locations, with the regions of interest encircled. The radius of each circle in the insets corresponds to the uncertainty range (0.4 mm in the original film) associated14 with the location of Canopus. If the image of Canopus had the same size as Venus in Apollo 14 photographs (Figure 12), its linear size in Figure 13 would be 1/10–1/15 of the diameter of the circle. Unfortunately, no image can be reliably distinguished inside the search area. The same is true for the zones surrounding this area: no light spots can be detected at any reasonable distance from the circles. The only possible explanation of our failure is that exposures of these photographs or their scans were insufficient for Canopus to be revealed.
Figure 13.

The expected locations of Canopus are depicted as circles in the enhanced insets from the photographs A11-40-5851 (a), AS11-40-5874 (b), AS11-40-5875 (c), and AS11-40-5944 (d). These circles are centered at the coordinates specified in Table 1 and have a radius of 0.4 mm. The predicted positions of Canopus are indicated in the full-size scans with white dots, where the size of each dot corresponds to 0.4 mm in the original film. The full-size scans used for this purpose are sourced from (LPI), while the insets are derived from high-resolution photos available in (NASA/JSC/ASU). © 2005 Lunar and Planetary Institute/Universities Space Research Association.

Figure 13.

The expected locations of Canopus are depicted as circles in the enhanced insets from the photographs A11-40-5851 (a), AS11-40-5874 (b), AS11-40-5875 (c), and AS11-40-5944 (d). These circles are centered at the coordinates specified in Table 1 and have a radius of 0.4 mm. The predicted positions of Canopus are indicated in the full-size scans with white dots, where the size of each dot corresponds to 0.4 mm in the original film. The full-size scans used for this purpose are sourced from (LPI), while the insets are derived from high-resolution photos available in (NASA/JSC/ASU). © 2005 Lunar and Planetary Institute/Universities Space Research Association.

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We also examined some color photographs from the Apollo 12 mission, which are listed in Table 1. However, the results were the same: it was impossible to distinguish Canopus from the background noise. Finally, we examined two black-and-white Apollo 12 photographs where Canopus might be present. We hoped that larger dynamic range and resolution of black-and-white photographs would increase our chances, but unfortunately, we were not successful. As shown in Figure 14, Canopus does not appear in the black-and-white photos either.151617
Figure 14.

Apollo 12 mission photographs with predicted locations of Canopus. The predicted locations are labeled with white dots. Strongly enhanced insets show the predicted locations in circles. The radii of both the dots and circles correspond to 0.4 mm in the original film. (a) corresponds to A12-47-6945, (b) corresponds to A12-47-6966 (both color photos), (c) corresponds to AS12-48-7042 with the SWC in front, and (d) corresponds to AS12-48-7140 (both black-and-white photos).

Figure 14.

Apollo 12 mission photographs with predicted locations of Canopus. The predicted locations are labeled with white dots. Strongly enhanced insets show the predicted locations in circles. The radii of both the dots and circles correspond to 0.4 mm in the original film. (a) corresponds to A12-47-6945, (b) corresponds to A12-47-6966 (both color photos), (c) corresponds to AS12-48-7042 with the SWC in front, and (d) corresponds to AS12-48-7140 (both black-and-white photos).

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5.2 Other Stars

After Canopus, the next brightest star that might potentially appear in Apollo 11 photographs is Achernar. However, it is approximately three times dimmer than Canopus, and we did not identify it. We did not attempt to search for any dimmer stars. The only planet that appears in Apollo 11 photographs is Earth.

In Apollo 12 photographs, the proximity of the Sun and the resulting glare made it difficult to capture α Centauri, the third brightest star, which is 1.5 times dimmer than Canopus. Other potential bright targets were Capella, Rigel, and Betelgeuse. Mercury was hidden in the solar glare, and other planets were too high or too low. We were unable to detect α Centauri in the color photo AS12-47-6992, nor Capella in the black-and-white photo AS12-48-7136.

In the Apollo 14 mission, the brightest star that may have potentially been featured in analyzed photos was Vega. We attempted to locate it in the color photograph AS14-66-9301 without success. As previously noted, Earth and Venus are clearly distinguishable in Apollo 14 photos. Other bright planets were not in suitable positions to be captured.

As1818 we have seen in Section 3.1, it is possible to insert virtual objects into19 the 3D-space of the Apollo landing sites and to add their images to lunar photographs. When we realized that stars cannot20 be revealed in available scans, we got an idea to “restore” starry sky views in some of the iconic photographs. To recreate these views, we used the Yale Bright Star Catalog (Hoffleit & Jaschek, 1991), as it is a mostly complete list of stars with apparent magnitudes up to mV=7. The catalog contains coordinates of stars, their names and catalog numbers, apparent magnitudes, spectral classes, and other data. Our code parses the catalog, chooses stars brighter than a predefined threshold, transforms their equatorial coordinates to the horizontal frame, and projects them as small disks onto the selected lunar images. The size of the disk and its color depend on the apparent magnitude and spectral class of the star (brighter stars are larger, dimmer stars are darker, and colder stars are redder). We also used data on constellation boundaries from Barbier (2022) to draw the stars in the corresponding context. Asterisms are drawn according to the O. Hlad sky culture in Stellarium. Images of the Sun and planets are also added where necessary, and the size of the Sun and Earth images corresponds to their actual distance at the instances the photographs were taken.

Another useful feature to represent graphically in lunar photographs is the astronomical horizon line, that is, the zero elevation line. The photograph may also be rotated to remove the tilt of the astronomical horizon. In this way, the actual tilt of the terrain is visualised. Cardinal points may also be added to give an idea about the azimuth. Some iconic photographs are presented here with restored stars, constellation boundaries, asterisms and the astronomical horizon line; see Figures 1519. The16 limiting17 apparent18 magnitude19 in these images is mV=5 in all photographs with the exception of AS12-47-6896, where the limiting magnitude mV=4 was chosen because of a large number of stars in the field of view. The images were rotated to remove the tilt of the astronomical horizon. Full-size color versions of these and some other images may be found in Pustynski (2023). The scans are from the Lunar and Planetary Institute. As our code draws stars and other objects over the whole field of view, we manually removed objects hidden behind the terrain, hardware, and astronauts.
Figure 15.

Little Dipper and Polaris in the background of Aldrin's egress, photograph AS11-40-5868. The visible horizon is slightly below the astronomical one as the terrain is slightly tilted in the NE direction. White horizontal line is the astronomical horizon, N points to the north.

Figure 15.

Little Dipper and Polaris in the background of Aldrin's egress, photograph AS11-40-5868. The visible horizon is slightly below the astronomical one as the terrain is slightly tilted in the NE direction. White horizontal line is the astronomical horizon, N points to the north.

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Figure 16.

Canopus shines right above the flag in the famous photograph AS11-40-5875 with Buzz Aldrin and the flag.

Figure 16.

Canopus shines right above the flag in the famous photograph AS11-40-5875 with Buzz Aldrin and the flag.

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Figure 17.

Buzz Aldrin deploying the seismometer, photograph AS11-40-5946. When the tilt of the astronomical horizon is removed, the slope of the landing site resulting in  4.5° tilt of the LM becomes evident.

Figure 17.

Buzz Aldrin deploying the seismometer, photograph AS11-40-5946. When the tilt of the astronomical horizon is removed, the slope of the landing site resulting in  4.5° tilt of the LM becomes evident.

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Figure 18.

Orion above Peter Conrad who stands near the flag, photograph AS12-47-6896.

Figure 18.

Orion above Peter Conrad who stands near the flag, photograph AS12-47-6896.

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Figure 19.

Alan Bean near Surveyor III with the LM in the background. Capella is above Alan's head. Photo AS12-48-7136.

Figure 19.

Alan Bean near Surveyor III with the LM in the background. Capella is above Alan's head. Photo AS12-48-7136.

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When we began this project, we hoped to identify at least the brightest stars and planets in Apollo photographs, based on the presence of Venus in all Apollo 14 photos. Our expectation was that we would be able to detect these stars as a group of several brighter pixels, given their brightness in comparison to Venus (which was 15 times brighter than Sirius and nearly 30 times brighter than Canopus, and it is represented by a group of several tens of pixels in the Apollo 14 photos). We used accurate values of camera rotations from the photogrammetric models of the Apollo 11–14 landing sites to calculate expected coordinates of the brightest stars in the image plane. However, Sirius and bright planets were outside the frame of the studied photographs, and Canopus was not revealed. Dimmer stars like α Centauri, Capella, and Vega were not detected either.

We believe that our failure cannot be attributed to inaccuracy of the models and the algorithm. Our accuracy tests show that the determined coordinates are accurate to at least 0.4 mm in the image plane of the original film, and the stars should indeed be inside the circles shown in Figures 1314. We suspect that the stars were not revealed due to insufficient exposure of the photographs or available scans. Many high-resolution scans in (NASA/JSC/ASU) are quite dark, and their dynamic range in sky areas is very small. It is possible that if these areas were scanned with brighter light settings or if the original films were studied with a microscope, there may still be a chance to find the brightest stars. We suggest using the coordinates from Table 1 to search for stars in Apollo 11 and Apollo 12 mission photographs. Apollo 14 photographs included in the model do not contain stars as bright as Sirius and Canopus inside the image frame. Accurate photogrammetric models of other landing sites are required to search for stars in photographs from the later missions.

We used our2122 code to recreate the starry sky in some iconic Apollo photos, but it can also be used to generate other visualizations unrelated to stars. One potential feature to add are coordinate grids that provide a visual representation of distances and azimuths, as shown in Figure 20. Keep in mind that coordinate lines may be situated above or below the lunar surface due to the uneven terrain. For example, the SWC pole is approximately 8.7 m away from the coordinates origin, but in Figure 20b it is projected closer to R=8 m line because of its elevated position.
Figure 20.

Cartesian (a) and polar (b) coordinates overlaid onto the photograph AS11-40-5873. In (a), the distance between the gridlines is 5 m, the maximum size of the grid is 100 × 100 m, and the x-axis points to the east. In (b), the distance between the circular lines is 2 m, the maximum radius of the grid is 20 m, azimuth lines are separated by 30°, and the 0° azimuth line points to the north. Both coordinate grids are flat, horizontal, and have zero elevation. The origin coincides with the midpoint of the LM landing pads. Keep in mind that as the terrain is uneven and the grids are flat, coordinate lines may be situated above or below the lunar surface.

Figure 20.

Cartesian (a) and polar (b) coordinates overlaid onto the photograph AS11-40-5873. In (a), the distance between the gridlines is 5 m, the maximum size of the grid is 100 × 100 m, and the x-axis points to the east. In (b), the distance between the circular lines is 2 m, the maximum radius of the grid is 20 m, azimuth lines are separated by 30°, and the 0° azimuth line points to the north. Both coordinate grids are flat, horizontal, and have zero elevation. The origin coincides with the midpoint of the LM landing pads. Keep in mind that as the terrain is uneven and the grids are flat, coordinate lines may be situated above or below the lunar surface.

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Terrain elevations and depressions can be visualized to study topography of the landing sites. Figure 21 shows an example of isohypses drawn inside the eastern component of Double Crater, a small crater to the southwest of the Apollo 11 LM, to illustrate its profile. To create this image, we first found the 3D coordinates of 130 points inside the crater. Then, we modeled this point cloud using a mesh of 230 triangles. Next, we remapped the model with isohypses: we found the intersection points of the mesh edges with horizontal planes and calculated the isohypses as cubic splines interpolating these intersection points in 3D space. Finally, we projected the splines onto the plane of the photographs.
Figure 21.

Isohypses inside the eastern component of Double Crater, as seen from the LM commander's window. The image was created by stitching together photographs AS11-39-5759 and AS11-39-5761 using Hugin Panorama Editor (https://hugin.sourceforge.io). The elevation difference between the lines is 20 cm, with zero elevation coinciding with the midpoint of the LM landing pads. Small craters inside Double Crater were intentionally ignored, as a higher number of points were required to achieve a higher spatial resolution.

Figure 21.

Isohypses inside the eastern component of Double Crater, as seen from the LM commander's window. The image was created by stitching together photographs AS11-39-5759 and AS11-39-5761 using Hugin Panorama Editor (https://hugin.sourceforge.io). The elevation difference between the lines is 20 cm, with zero elevation coinciding with the midpoint of the LM landing pads. Small craters inside Double Crater were intentionally ignored, as a higher number of points were required to achieve a higher spatial resolution.

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Augmented reality based on Apollo imagery can also serve for study purposes. For example, animations of virtual objects moving in lunar gravity can be created, taking into account a range of physical factors such as the rotation of free bodies, surface reflectance, and changing shadows. In Figure 22, we present four frames from an animation of a cuboid that is both moving and rotating above Double Crater. The object is assumed to be in free fall with an initial positive vertical velocity, and the simulation assumes Lambertian reflectance and illumination that corresponds to the actual solar position, with lunar surface illumination also accounted for in a rough approximation. Torque-free rotational motion is not modeled accurately. The grey solid line indicates the trajectory of the center of mass. The shadow cast on the bottom of Double Crater is modeled based on the same terrain model as Figure 21. The complete animation can be found in Pustynski (2023).
Figure 22.

Four individual frames from an animation of a cuboid 0.41 × 0.86 × 0.26 m moving and rotating in the lunar gravity field. The photo AS11-40-5889 was used for this simulation, and the movie is slowed down 5 times for ease of viewing.

Figure 22.

Four individual frames from an animation of a cuboid 0.41 × 0.86 × 0.26 m moving and rotating in the lunar gravity field. The photo AS11-40-5889 was used for this simulation, and the movie is slowed down 5 times for ease of viewing.

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Below are some potential applications of augmented reality based on lunar photos:

  • Virtual objects can be inserted into the landing site's 3D space, and their views from various camera stations can be simulated. As an example, we provide in Pustynski (2023) a couple of photographs featuring a virtual stadiometer set at the ground near an astronaut figure, which can be used to easily estimate the astronaut's height. If accurate models of the terrain are available, shadows of these objects can also be modeled, as shown in Figures 7 and 22. To achieve more natural visualization, the actual position of the Sun and reflectance of the terrain may be considered for more precise modeling of shades and colors.

  • Animations can be created to demonstrate the motion of virtual objects as they are viewed from different camera stations, for instance, animations of rocks launched and moving in lunar gravity, or the LM during landing and launch, etc. These animations can be interactive, allowing the user to define coordinates of the launch point, initial velocity vector and rotations, object dimensions, etc.

  • Views from virtual camera stations can be simulated, where no actual photographs were taken. To generate these views, highly detailed photogrammetric models of artifacts and terrain should be constructed, with textures either modeled or partially obtained from Apollo photographs. An example of such digital model can be found in Le Mouélic et al. (2020).

  • A virtual planetarium can be developed to display positions and movements of celestial bodies as viewed from various camera stations. To accomplish this, the illumination of the terrain and hardware must be modeled for different solar elevations (to simplify this task, actual objects may be replaced by 3D models).

The computer code used to compile graphics for Apollo photographs (e.g., stars, constellations, contour lines) can be found in Pustynski (2023), which includes a comprehensive guide.

This study was conducted as part of the author's research work in Tallinn University of Technology (Taltech). The author would like to thank Siim Pugal for his assistance in compiling the photogrammetric model of the Apollo 14 landing site. The author expresses sincere gratitude to the anonymous reviewers whose remarks and valuable advice have contributed to the improvement of this manuscript.

The data supporting the findings of this study, including camera coordinates, rotations, and the computer code used for visualizations, are openly accessible in the Mendeley Data repository (Pustynski,222023).

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Author notes

All Lunar and Planetary Institute images are © 2005 Lunar and Planetary Institute/Universities Research Association.