Descent trajectory reconstruction and landing site positioning of Chang'E-4 on the lunar farside.

Chang'E-4 (CE-4) was the first mission to accomplish the goal of a successful soft landing on the lunar farside. The landing trajectory and the location of the landing site can be effectively reconstructed and determined using series of images obtained during descent when there were no Earth-based radio tracking and the telemetry data. Here we reconstructed the powered descent trajectory of CE-4 using photogrammetrically processed images of the CE-4 landing camera, navigation camera, and terrain data of Chang'E-2. We confirmed that the precise location of the landing site is 177.5991°E, 45.4446°S with an elevation of -5935 m. The landing location was accurately identified with lunar imagery and terrain data with spatial resolutions of 7 m/p, 5 m/p, 1 m/p, 10 cm/p and 5 cm/p. These results will provide geodetic data for the study of lunar control points, high-precision lunar mapping, and subsequent lunar exploration, such as by the Yutu-2 rover.

In the discussion section: the comment about the gentle topography (L173) for the Chang'E-4 site compared to the Chang'E-3 site lacked sufficient detail to draw effective conclusions. A 3km variation vs a 6000m (please use the same units) does not seem like a drastic enough change. It seems like there was something significant, but the text was hard to follow. The phrase "avoid the discontinuity" (L176) needs more clarity.
L87 More information about the Automatic on-orbit analysis would be useful, either here or in methods. Is this software available? Does it have a name? Has it been used before?
L109 More information about the three-dimension laser imaging should be provided.
L139 Figure 4 shows a shaded relief map of the landing site. This shaded relief map has significant pixelation and artifacts (surface is too flat, lack of craters near the site, etc.) Can you provide any discussion for this? Also, it would be useful to have an image that shows which regions where done at what resolution. While the text says 2cm DEM were produced, I expect that wasn't done over all of the region. Thus, showing where the data has higher resolution would improve people's understanding of the process and where the data is best.
L146 How was the 5 laser reflectors integrated into your analysis? How where they measured? When where these measurements taken?
L233 More discussion about why LROC positions are so different than Chang'E-4 would be useful. L245 Define RANSAC L250 What is a vertical ground control point. L256 Define EO L270 Define TIN L271 Define LACM, or did you mean LCAM?
Minor Comments L14 successful should be successfully L17 Recommend changing "real time" with "a" (It wasn't real time when the reconstruction was done) L28-31 Sentence "After…" is awkward. Suggest replacing "experienced" with "conducted". "descending" with "descent" L31 Remove comma after Moon L45 Define DOM and DEM L49 Suggest replacing "Combined with the" with "Using combined" L59 Caption. Suggest adding a comment that the + is the identified landing location L70 Only use etc. for a list of items that are known. If you are making a list of items, give the full list. In this case, you might be able to remove etc altogether. L78-82 Awkward sentence. This may be because the concept of vertical attitude isn't defined. L81 Likewise "horizontal to the vertical direction" isn't clear L89 Sentence starting with "Therefore…" is confusing. L93 After hovered, replace comma with "and" L113 Can you provide the speed of the "slow vertical descent?" L117 Provide a reference for the bundle adjustment technique. L123 Either provide the residuals for the bundle adjustment here or refer readers to the method section. Table 1. Suggest putting error values next to the lat/lon rather than in comments L157-159. I suggest putting a dashed line around the next image's footprint. It would make it easier for people to follow the progress of images. Thus, image C would have a small box that matched the full field of view of image D. Also, a scale bar on each would be beneficial. L189-192 Suggest referring the reader to the methods section to understand where the RMS error comes from. L195-196 Sentence starting with "Apparently, …" is awkward. L232 Where are the reflectors located? Are they on the near or far side? If so, how sampled? Eric E. Palmer Reviewer #2 (Remarks to the Author): Review of Paper "Descent Trajectory reconstruction and landing site positioning of Chang'E-4 on Moon's farside" by Jianjun Liu and Co-authors This is a most interesting report on the first historic landing on the lunar far-side, quite appropriate for publication in Nature.
However, the text would benefit from improvements. While the spelling is good, the wording and phrasing need some more work effort. Many sentences are not sufficiently specific. Besides, the text leaves some open questions. There is confusion about the instruments and the data that were used. Some critical information is only given late in the paper and should be moved up.
From the reading, I have the impression that in many places the paper is researching what the spacecraft was doing. I suggest to improve the phrasing to correct this impression.
I tried to point out problems and make some suggestions, see my comments below.
Generally speaking, I recommend publication of the exciting material, pending on a number of improvements of the text.

Specific comments:
Title: ..on Moon's farside --> ..on the Moon's farside (or: on the lunar farside) Abstract: Because it is impossible to directly measure the farside of the Moon ... --> As Earth-based radio tracking is impossible for a spacecraft moving over the lunar farside ... to use real-time series of image data --> to use image data obtained during descent, which were transmitted to the ground after landing via a relay satellite (perhaps you may want to give the name of the satellite and mention its important mission) It was found that CE-4 … realized a safe soft landing --> it seems that the paper is researching what the spacecraft was doing. I suggest to rephrase this (and in other places the main text of the paper.) L 34 -37 It is impossible to perform… real-time control based on the measurement and control network of earth --> ? not clear, need to rephrase L 40 It is expected that slight movement … --> We reconstructed the descent trajectory, showing even barely perceivable maneuvers of the spacecraft during the landing approach (ok?) L 45 --> please explain to the non-expert reader: what are DOM and DEM? L 67 One general comment: It is not clear what is described in this chapter. Is it the trajectory from the autonomous navigation or is it the reconstruction of the trajectory from the images, after the landing. The topic of trajectory reconstruction is only introduced later in the paper.

L 72
Autonomous navigation control was adopted in the whole landing process --> there is little information in the paper. Did the autonomous navigation use the LCAM images? General question: Is the information on the autonomous navigation solution available, and was it used in the reconstruction of the trajectory? L 73 obstacle avoidance --> How was this accomplished? L 78 … started acquiring image … --> started acquiring images … (or: acquired the first image…) … started acquiring image 5m11s … after onset of CE-4 power descent --> Can you give more information? What was the time of the touch-down? L 109 laser imaging sensor --> can you explain? L 115 General question: "We made LCAM topographic maps" --> considering that the LCAM images were all taken from above, stereo angles between images were probably very small. How did you manage to produce the topography?
Were topographic maps produced after the trajectory reconstruction, assuming that the spacecraft position and attitude were fixed for each image? Or was this a combined approach?
Were the laser images available to support the map production? The plot combines topography and spacecraft height. Would it make sense to show topography and spacecraft height separately? L 174 our results reveal that the spacecraft switched from oblique downward to vertical downward… --> not clear (it seems that the paper is researching what the spacecraft was doing) L 176 … which effectively avoid the discontinuity --> discontinuity? not clear … which effectively avoid --> … which effectively avoided L 178 distance measuring sensor --> can you explain? General question: were the data from distance measuring sensor and the above mentioned laser imaging sensor used in the reconstruction of the trajectory? (Note that these instruments are not listed in the "Instrument Description") L 186 Based on the sequence images of the LCAM, we reconstructed the power descent trajectory of the CE-4 lander through the photogrammetry method --> this is coming very late (in the Discussion?). If I understand correctly, results are already shown earlier in the paper.
L 191 and L 232: CE2TMap2015 absolute accuracy... --> how did the map achieve this excellent accuracy? Unfortunately, the relevant papers that are referenced are all in Chinese.
L 195: Why is the difference in position so large? Does it mean that the LRO reference frame and CE2TMap2015 differ by ~500m? It seems there is some confusion about the reference frame in use.
L 206 Instrument descriptions --> This information is coming very late in the paper. The complete list of instrument and relevant data used in the analysis should be briefly introduced earlier in the paper. The details may be moved to the end. It appears that critical instruments are not listed (laser imager, distance sensor?) L 249: what is the NAC image used for? It is also not mentioned in Fig.7? Please clarify L 369 We thank the team ... --> perhaps this statement should go into the acknowledgements?
Reviewer #3 (Remarks to the Author): The manuscript submitted by Liu et al presents the photogrammetric methodology utilized to determine the descent trajectory and surface coordinates of the Chang'e 4 lander. 1) What are the major claims of the paper? -The authors derived a detailed reconstruction of the descent trajectory, which included autonomous hazard avoidance. They describe how the onboard systems avoided hazards and allowed the vehicle to land safely on the lunar farside. The trajectory and surface coordinate reconstructions were the result of standard photogrammetric bundle block adjustment techniques.
The authors provide the following coordinates for the lander 45.4446°S latitude, 177.5991°E, elevation -5935 meters and state that (lines 199-201) "As a permanent artificial landmark on the farside of the Moon, the location of the CE-4 lander was precisely confirmed using CE-2 and CE-4 image, and can serve as a potential control point on the farside of the Moon." Absolute coordinate control for the Chang'e 4 images was provided by tying the bundle block adjustment to the Chang'e 2 global image mosaic / control network, with a stated uncertainty of 21-97 m horizontal and 2-19 m elevation. The Chang'e 2 coordinate system is in turn tied to the 5 laser retroreflectors located on the nearside. Note that in the caption to Table 1 a footnote states (line 149): "...the elevation data was accurate to meter." It is not clear to the reviewer where the accurate to a meter was derived when previously it was stated that the uncertainty in elevation was 2-19 m.
The authors compared their derived coordinates to those derived by the Lunar Reconnaissance Orbiter Camera (LROC) team values (45.457°S, 177.589°E, plus minus 20 meters) and state that there is a 376 m and 215 m difference in latitude and longitude (respectively), for a total 433 m positional offset. The authors state that: "The total positional deviation is 433 m. Apparently, the positioning data of this study is more sufficient and detailed, and the results are more accurate. The latitude and longitude disagreement with that of LRO data can be accounted for by different reference map."  [Note: a degree on the Moon is ~30.3 kilometer so 0.001° is ~30 meters] 2) Are they novel and will they be of interest to others in the community and the wider field? -While the methods presented in this work to derive the trajectory and lander coordinates are not novel, the reconstruction of a robotic lander under autonomy as it sets down on the lunar farside is novel and will be of interest to others in the community and the wider field.
3) If the conclusions are not original, it would be helpful if you could provide relevant references. The conclusions seem to be original, though partially unsubstantiated. Authors might add a standard reference to the bundle block adjustment technique that goes back 60 years (see below). 4) Is the work convincing, and if not, what further evidence would be required to strengthen the conclusions? -For the most part the work is convincing. I do have one quibble with the comparison to the LROC team coordinates of the lander summarized above (see also lines 194-198 in manuscript). One could justifiably argue that the CE-2 coordinate system tied to the 5 nearside retroreflectors will not be as accurate on the opposite side of the Moon for several reasons (i.e. the lumpy gravity field of the Moon, small uncertainties in camera model (distortion, FL) adding up over "distance", etc.). For example, a control network derived from Clementine UVVIS images was also shown to have km offsets due to the aforementioned reasons (Speyerer et al., 2016).
The authors did not fully document the coordinate system used in their work (a key reference is in Chinese and this reviewer was unable to read the paper) thus the claim that discrepancy is due to "different reference map" is left ambiguous. The LROC coordinates derived have a stated accuracy much smaller than the 433 meters reported in this manuscript.
Mazarico, E., Goossens, S.J., Lemoine, F.G, et al. , 2013. Improved orbit determination of lunar orbiters with lunar and gravity fields obtained by the GRAIL mission. In: Proceedings of the 44th Lunar and Planetary Science Conference. The Wood-lands, TX, Abstract #2414. Speyerer, E.J., Wagner, R.V., and Robinson, M.S., 2016. Geometric Calibration of the Clementine UVVIS Camera Using Images Acquired by the Lunar Reconnaissance Orbiter. In: The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI- Yes, different reference maps were used: LOLA vs Chang'e 2 for the LROC vs Chang'e 4 work. The manuscript does not in any way document the assertion: "Apparently, the positioning data of this study is more sufficient and detailed, and the results are more accurate." The authors need to compare the Chang'e 2 coordinate system with the LOLA system in a global sense and make some quantitative assessment of any discrepancies between the two products to support the statement quoted above (lines 195-196 in the manuscript). 5) On a more subjective note, do you feel that the paper will influence thinking in the field? The description of the descent trajectory and derivation of the coordinates is certainly of broad interest, however I do not think the manuscript will influence thinking in the field.
General Comments To Authors 1) There are a few instances of inappropriate word usage and faulty grammar, likely due to translation to English. Some logical inconsistencies may wholly or partially be due to a language issue.
Examples: 1) Line 15 16: "Because it is impossible to directly measure the farside of the Moon, we cannot acquire the descent trajectory and the landing site of the spacecraft." It is possible to directly measure the lunar farside and the Chinese L2 relay satellite Queqiao should have been able to receive telemetry during the descent I cannot understand what is meant by this sentence. I can guess, but the authors should clarify. Perhaps the lander did not have the ability to transmit to Queqiao during the descent?
2) Please spell out terms before using abbreviations/acronyms (i.e. DOM, DEM) 3) "farside of the Moon" appears multiple times. After the first instance you can drop the "of the Moon" and just say farside. 4) "5m/p, 1m/p, 10cm/p, 5cm/p resolution" appears multiple times throughout the manuscript. Once or twice is plenty. Table 4 and 5 (and elsewhere in the manuscript) may be overly precise. Are three decimal places really justifiable (mm precision)? First of all, we sincerely thank the reviewers for their critical reading of our manuscript, which help to significantly improve our manuscript. We addressed all remarks made by the 3 reviewers. Our responses are given in red below each remark. The paper is well written and clear with only a few awkward sentences.

5) The values in
The paper does a good job describing the sequence of events and the data that was available to the spacecraft and later the reconstruction team. The reviewer would have liked to see more detail in the method section of the specific mathematics and techniques used, especially the bundle adjustment applied.

Response：
According to the reviewer's opinion, we added a detailed description of the bundle adjustment theory in the "Methods" section. The original L253~L258 is revised as follows.
"According to photogrammetric bundle adjustment theory 22,23 where (x, y)  In the discussion section: the comment about the gentle topography (L173) for the Chang'E-4 site compared to the Chang'E-3 site lacked sufficient detail to draw effective conclusions. A 3km variation vs a 6000m (please use the same units) does not seem like a drastic enough change. It seems like there was something significant, but the text was hard to follow. The phrase "avoid the discontinuity" (L176) needs more clarity.

Response：
Thanks to the reviewer for his meticulous work. In order to draw our conclusions more clearly and effectively, the manuscript has been improved and supplemented accordingly.
(1) In Figure   (2) The description in discussion section was revised.  (3)The unit of elevation variations in the manuscript has been changed to "meter". The phrase "avoid the discontinuity" (L176) is deleted.
L87 More information about the Automatic on-orbit analysis would be useful, either here or in methods. Is this software available? Does it have a name? Has it been used before?
L109 More information about the three-dimension laser imaging should be provided.

The Automatic on-orbit control technology and sensors including the laser imaging sensor of CE-4 is similar to Chang'E-3 (CE-3). We have added a brief introduction in the
manuscript "Discussion" section with the following reference (Li et al., 2016). L146 How was the 5 laser reflectors integrated into your analysis? How where they measured? When where these measurements taken?

Response：
The lunar position of these five laser reflectors is not directly used in the analysis of this paper, but is used to illustrate the absolute positional accuracy of CE2TMap2015. In addition to the reference (Li et al., 2018) in Chinese, two English references have been supplemented in this manuscript as supporting materials for CE2TMap2015 accuracy.
The size of the laser reflector is less than 1 m, which cannot be recognized on current high-resolution lunar remote sensing images, while the lander or lunar rover can be identified on the image. In 2010, the recognition results of the five lunar modules on the LRO narrow-angle camera 0.5m resolution image is published on the NASA official website. According to the relative positional relationship between the laser reflector and the lunar module, (Williams et al., 1996 and2004;Murphy et al., 2011;Wagner et al., 2012) calculated the lunar surface position of these lunar modules corresponding to the laser reflectors. The positioning accuracy is about 30m. We used CE-2 7m resolution image to register with the LRO narrow-angle camera 0.5m resolution image to determine the pixel position of the laser reflector on CE2TMap2015. Then the absolute positional accuracy of the moon surface of CE2TMap2015 is obtained (Yan et al, 2015;Li et al., 2018;Ren et al, 2019).
Related references are as follows.

Response：
The more discussion is added in the manuscript L233 and Methods.
The LROC positioning results are so different from the results in this study because there are differences in the absolute positions of the two sets of data products. Li et al., (2018) and Ren et al. (2019) .

Response：
The full name of RANSAC is added in the manuscript, i.e. random sample consensus.
RANSAC is a random sampling consistency algorithm, which is based on a set of sample data sets containing abnormal data, calculates mathematical model parameters of the data, and obtains effective sample data. In the image matching process, it is commonly used as an algorithm for erroneous matching point culling.
L250 What is a vertical ground control point.

Response：
Here, the sentence should be vertical control point.
The ground control points (GCPs) in the photogrammetric processing generally includes

Response：
There is a spelling mistake. It should be a "LCAM" here.
Minor Comments L14 successful should be successfully L17 Recommend changing "real time" with "a" (It wasn't real time when the reconstruction was done) L28-31 Sentence "After…" is awkward. Suggest replacing "experienced" with "conducted". "descending" with "descent" L31 Remove comma after Moon L49 Suggest replacing "Combined with the" with "Using combined" L70 Only use etc. for a list of items that are known. If you are making a list of items, give the full list. In this case, you might be able to remove etc altogether.
L93 After hovered, replace comma with "and"

Response：
The manuscript has been revised according to the reviewer's comments.  L123 Either provide the residuals for the bundle adjustment here or refer readers to the method section.
Related references are as follows: There is confusion about the instruments and the data that were used. Some critical information is only given late in the paper and should be moved up.

Response：
This work is focused on the descent trajectory reconstruction using high-frequency

Response：
The manuscript has been revised according to the reviewer's comments. Is it the trajectory from the autonomous navigation or is it the reconstruction of the trajectory from the images, after the landing. The topic of trajectory reconstruction is only introduced later in the paper.

Response：
The main purpose of this study is to reconstruct CE-4 powered descent trajectory using Autonomous navigation control was adopted in the whole landing process --> there is little information in the paper. Did the autonomous navigation use the LCAM images?
General question: Is the information on the autonomous navigation solution available, and was it used in the reconstruction of the trajectory?

Response：
The LCAM images were not used in the autonomous navigation process, but they completely recorded the entire powered descent process of the CE-4. This is why we used the LCAM images to reconstruct the powered descent trajectory.  (Li et al., 2016).

Because the Automatic on-orbit control technology and navigation system sensors of CE-4 are similar to Chang'E-3 (CE-3), the specific implementation process of the obstacle
avoidance process also can be found in the above reference.

The detailed process of the CE-4 on-orbit autonomous navigation is no longer described in this manuscript, and only the characteristics of the powered descent trajectory
reconstruction results are analyzed. This sentence has been deleted in the manuscript.

The Automatic on-orbit control technology and sensors including the laser imaging sensor of CE-4 is similar to Chang'E-3 (CE-3). We have added a brief introduction in the
manuscript "Discussion" section with the following reference (Li et al., 2016

The Automatic on-orbit control technology and sensors including the laser imaging sensor of CE-4 is similar to Chang'E-3 (CE-3). We have added a brief introduction in the
manuscript "Discussion" section with the following reference (Li et al., 2016).  Table 4 is also revised. On the other hand, the number in the Figure 3 (b) is changed to "NGCP01, NGCP02... Table 5 is also revised.

Response：
The manuscript has been revised according to the reviewer's comments.

L 167
Discussion --> It is strange to have the discussion so early, even before description of Methods.

Response：
According to the format requirements of the Nature communication journal, the "Methods" section should be described after the conclusion and discussion section as supporting materials.

L 171
It is confusing to mix discussions of CE4 and CE3. What are we to learn from CE3 here?

Response：
In order to eliminate confusion, the details description has been revised in the "Discussion"

section. The difference in the powered descent trajectories of CE-3 and CE-4 is mainly
discussed.

We compared the trajectory and nadir trace elevation variations of CE-3 with that of CE-4,
and found that the change of the CE-4 orbital strategy mainly results from the terrain variation. This strategy shows a good performance in the CE-4 mission. Thus, consideration of the terrain variation when formulating the orbital strategy is important for future safe soft landing on the planet surface.

Response：
The manuscript has been revised according to the reviewer's comments.

The Automatic on-orbit control technology and sensors including the laser imaging sensor of CE-4 is similar to Chang'E-3 (CE-3). We have added a brief introduction in the
manuscript "Discussion" section with the following reference (Li et al., 2016).

Response：
The photogrammetry method which used in the trajectory reconstruction in the study has been mentioned in the introduction section. The detailed information about this method is described in the "Methods" section.
--> how did the map achieve this excellent accuracy? Unfortunately, the relevant papers that are referenced are all in Chinese.

Response：
The absolute accuracy of CE2TMap2015 has been achieved by global adjustment using CE-2 Stereo images. We added two English references as follows in the manuscript to make the readers understand the detailed process of the method clearer. L 195: Why is the difference in position so large? Does it mean that the LRO reference frame and CE2TMap2015 differ by ~500m? It seems there is some confusion about the reference frame in use.

Response：
The same lunar coordinate system is used for CE2TMap2015 and LRO data, i.e. the mean Earth/polar axis coordinate system. The reference surface of the elevation is the surface of the Moon's spheroid with a radius of 1737.4 km, and the reference origin is the mass center of the Moon.
In line 195 in the manuscript, the planimetric deviation is 433 m between the positions calculated from CE2TMap2015 and LRO data. The deviation is mainly due to the absolute position between these two data. Here, a new reference has been referenced to main text (Ren et al., 2019, in press).
Three-dimensional orbital positions are important input parameter for the lunar terrain reconstruction. There are some system deviation between these orbital positions of CE-2 and LRO because of many reasons, such as the orbit calculation models of CE-2 and LRO, the gravity field model (CE-2 using the LP165P, the LRO using the GRAIL model), the accuracy of the ground radio measurements, and the orbital extrapolation method, etc.
Corresponding, there are some positional deviation between the CE2TMap2015 and the LRO terrain data, which calculated using these orbital positions.
In order to calculate the planimetric deviations between LRO data (GLD100m) and CE2TMap2015

The Automatic on-orbit control technology and sensors including the laser imaging sensor of CE-4 is similar to Chang'E-3 (CE-3). We have added a brief introduction in the
manuscript "Discussion" section with the following reference (Li et al., 2016).
Li, S., Jiang, X. Q., Tao, T. Guidance Summary and Assessment of the Chang'e-3 Powered Descent and Landing. JOURNAL OF SPACECRAFT AND ROCKETS. 53 (2): 258-277(2016) L 249: what is the NAC image used for? It is also not mentioned in Fig.7 GCPs for the LCAM images, whose resolution is better than 1m, was firstly identified on the rectified LRO NAC image. Then, the planimetric position and elevation was measured from the CE2TMap2015 map. In Fig. 7, we added this processing flow.
L 369 We thank the team ... --> perhaps this statement should go into the acknowledgements?

Response：
We accepted the reviewer's suggestion. The sentence "We thank the team ..." has gone into the acknowledgements. Considering there is no need to introduce the absolute accuracy of CE2TMap2015 here, and in order to avoid misunderstandings, we removed these contents in the main text, and introduced these contents in the section of "Instruments and dataset descriptions" in methods.
The authors compared their derived coordinates to those derived by the Lunar Reconnaissance Orbiter 2) Are they novel and will they be of interest to others in the community and the wider field?
-While the methods presented in this work to derive the trajectory and lander coordinates are not novel, the reconstruction of a robotic lander under autonomy as it sets down on the lunar farside is novel and will be of interest to others in the community and the wider field. The conclusions seem to be original, though partially unsubstantiated. Authors might add a standard reference to the bundle block adjustment technique that goes back 60 years (see below).

Response：
We added the following reference in the manuscript according to the reviewer.  194-198 in manuscript). One could justifiably argue that the CE-2 coordinate system tied to the 5 nearside retroreflectors will not be as accurate on the opposite side of the Moon for several reasons (i.e. the lumpy gravity field of the Moon, small uncertainties in camera model (distortion, FL) adding up over "distance", etc.). For example, a control network derived from Clementine UVVIS images was also shown to have km offsets due to the aforementioned reasons (Speyerer et al., 2016).
The authors did not fully document the coordinate system used in their work (a key reference is in Chinese and this reviewer was unable to read the paper) thus the claim that discrepancy is due to "different reference map" is left ambiguous. The LROC coordinates derived have a stated accuracy much smaller than the 433 meters reported in this manuscript.
Lunar Reconnaissance Orbiter radiometric tracking data were combined with the GRAIL gravity model to significantly improve the Lunar Reconnaissance Orbiter spacecraft ephemeris and thus geodetic accuracy of each LOLA spot to less than 10 m horizontally and 1 m vertically (Lemoine et al. 2014;Mazarico et al. 2012;Mazarico et al. 2013   Chang'e 2 coordinate system with the LOLA system in a global sense and make some quantitative assessment of any discrepancies between the two products to support the statement quoted above (lines 195-196 in the manuscript).

Response：
The results of (Yan et al, 2015;Li et al., 2018;Ren et al, 2019) show that the average planimetric and height deviations between neighboring strips of CE2TMap2015 were 5 m and 2 m (＜1pixel, with a spatial resolution of 7 m). (Lemoine et al. 2014;Mazarico et al. 2012;Mazarico et al. 2013) (Li et al., 2018;Ren et al, 2019 5) On a more subjective note, do you feel that the paper will influence thinking in the field?
The description of the descent trajectory and derivation of the coordinates is certainly of broad interest, however I do not think the manuscript will influence thinking in the field.

√
General Comments To Authors 1) There are a few instances of inappropriate word usage and faulty grammar, likely due to translation to English. Some logical inconsistencies may wholly or partially be due to a language issue. 3) "farside of the Moon" appears multiple times. After the first instance you can drop the "of the Moon" and just say farside.

Response：
The manuscript has been revised according to the reviewer's comments. Again, this is a most interesting report on the first historic landing on the lunar far-side, quite appropriate for publication in Nature.

5) The values in
The authors have responded very effectively on the comments by the referees. Also, wording and phrasing has very much improved.
I only have minor comments and remaining requests for clarifications. I recommend publication of the exciting material, pending on these clarifications.

Specifically:
Abstract series of image data --> series of images radio measurements --> radio tracking using photogrammetric processed images --> using photogrammetrically processed images --> (or) using photogrammetric image processing techniques It is almost the only effective way to reconstruct … --> We effectively reconstruct ...  The landing position was determined according to (a), and the position of the lander's leg was judged by (b).
--> While landing position was determined from orbital data (a), the orientation of the lander was determined using images taken from the ground (b).
Text above Fig. 6: the lander attitude was adjusted to a vertical attitude (?) --> the lander attitude was adjusted to enable thrusting for near-vertical descent Please add: Elevation is given with respect to … (?) Page 12 and Fig. 9: Perhaps, it is better to say: stones -> rocks The authors have not adequately responded to the biggest issue: Their implication that the 433 meter discrepancy between the manuscript coordinates and the LROC team coordinates for the Chang'e 4 lander can be explained by a more accurate Chang'e 4 derivation (and other associated mission data).
Text from the rebuttal.
"Therefore, the position of the CE-4 landing site determined in this study is authentic, which can reveal the actual position on the lunar farside. At the same time, in order to easily find the position of the CE-4 landing site, the pixel coordinates of the landing site were given in multiple LCAM images, which will be convenient for subsequent applications.
In lines 195-196 of the manuscript, we change old description ("obviously, the positioning data of this study is more complete and detailed, the results are more accurate.") to "The position of the CE-4 landing site determined in this study is authentic, which can reveal the actual location on the lunar farside. In this study, the CE-4 descent trajectory was recovered, and the landing site position was accurately determined. The pixel coordinates of the landing site were given in multiple LCAM images." From the revised manuscript lone 203: "...and the landing site position was accurately determined." [Note -I do not understand the use of the word authentic in the rebuttal and the revised manuscript, I think this might be a translation issue?] -The authors state that the absolute uncertainty of their reference frame is "decameter level" (line 312). (Reference 21 says "21-97 m" as does the methods section.) -The reviewer originally pointed out that the LROC frame of reference uncertainty is about 20 meters (though the manuscript under review does not mention that fact). See the papers mentioned in the original review that document the coordinate framework for LRO (Lemoine et al. 2014;Mazarico et al. 2012;Mazarico et al. 2013) and LROC (Speyerer et al., 2016, Wagner et al 2017, Henriksen et al 2017. -The authors acknowledge that the LROC team coordinates disagree by 433 m from their estimate (line 200), and state that this is "within the positional deviation range between the CE2TMap2015 and LRO terrain data [20,21] (see Methods section for details)." (Note: The Methods section says nothing about the LRO coordinate reference frame.) http://ch.whu.edu.cn/EN/volumn/volumn_1422.shtml -Reference 21 (http://ch.whu.edu.cn/EN/volumn/volumn_1422.shtml) does seem to be the source of their statement that the LRO and Chang'2 laser coordinates agree within uncertainty. Reference 21 also has a figure (pasted below) that shows that either the CE2TMap2015 or the GLD100/LOLA DEMs are grossly in error on the farside, disagreeing bỹ 500 m horizontally over the CE-4 landing site (and at least that much over most of the much of the farside). Neither reference 21 nor the paper under review give any rationale for why they assume that CE2TMap2015 is more accurate. Note that Reference 20 is in press and not available to this reviewer. Li, C. L., Liu, J. J., Ren, X., et al. Lunar Global High precision Terrain Reconstruction Based on Chang'e-2 Stereo Images. Geomatics and information Science of Wuhan University . 43 (4): 486-495 (2018). Note that Google Translate was used to help this non-Chinese reading reviewer read the publication.

Figure 3 and 4 from
Bottom line: The authors have not adequately responded to the biggest issue: Their implication that the 433 meter discrepancy between the manuscript coordinates and the LROC team coordinates for the Chang'e 4 lander can be explained by a more accurate Chang'e 4 derivation (and other associated mission data). Note: There is no need to give the scale bar (0, 100, 200 m) when the relevant data are obvious from the axes.

Response：
The axis is labeled with unit "m" and the North direction is marked in Fig. 1d and e. The scale bar is deleted in these figures. Fig. 4b: numbers on the color-bar: Shouldn't the elevation be km?
Considering the elevation profile given in Fig 6: wouldn't it be useful to show the approach trajectory on Fig. 4b?

Response：
The elevation is in meters in Fig. 4b. The approach trajectory is added in Fig. 4a and b according to the reviewer's comments.

Response：
The white rectangle in Fig. 4c represents the border of Fig. 4d. Because Fig. 4c is obtained at a higher altitude than Fig. 4d, the resolution of 4d is better than the resolution of 4c. We have revised the textual description of the manuscript to make it more clearly. "and the white borders in (c), (d), and (e) represent the positions of (d), (e), and (f) in the images, respectively."is revised to"and the white rectangles in (c), (d), and (e) represent the borders of (d), (e), and (f), respectively." Because Fig. 4c is obtained at a higher altitude than Fig. 4d, 4e, 4f, it can cover larger areas. Coverage area of Fig. 4c, 4d, 4e, 4f are 5km×5km、1km×1km、100m×100m、 50m×50m, respectively. The features of the lunar surface expressed in these figures will be significantly different.
Please check numbers on scale bars. Shouldn't the scale bar in 4c be in km? Fig. 4c is revised. The scale bar is in meters. Fig. 5 b. It is not clear, where the North arrow is pointed in this perspective viewing. Looking at Fig. 5a: From where was the image 5b taken? Which one is the crater in the background seen in 5b?

Response：
The lander side with red flag faces to North in this perspective viewing. Figure 5b is obtained by panoramic camera (PCAM) when the Yutu-2 rover moved to the northwest of the lander. In the revised manuscript, the location of Yutu-2 rover is marked as "#" in Fig.  5a and as a 3D model in Fig. 5d (original Fig.5c). The distance between the rover and the lander is about 18m at that time. Since the 5 craters marked in Figures 5a and 5d are far from the lander (more than 20m), the craters can't be seen in the PCAM's field of view.
CE-4 landing site can be also located in the Lunar Reconnaissance Orbiter (LRO) narrow angle camera (NAC) images, whose relative position to the surrounding terrain is consistent with our results. LRO NAC image of the CE-4 landing site collected on 1 February 2019 (M1303640934LR) is added as Fig.5c.

Response：
The manuscript has been revised according to the reviewer's comments. The location of Yutu-2 rover is also marked in the revised manuscript. Fig. 3d is used to describe the location of CE-4 landing site on the DOM produced by landing camera images.
The landing position was determined according to (a), and the position of the lander's leg was judged by (b).--> While landing position was determined from orbital data (a), the orientation of the lander was determined using images taken from the ground (b).

Response：
The manuscript has been revised according to the reviewer's comments.
Text above Fig. 6: the lander attitude was adjusted to a vertical attitude (?) --> the lander attitude was adjusted to enable thrusting for near-vertical descent

Response：
The manuscript has been revised according to the reviewer's comments.
Please add: Elevation is given with respect to … (?)

Response：
The manuscript has been revised according to the reviewer's comments. "Elevation is given with respect to the Moon's spheroid with a radius of 1737.4 km." is added in the revised manuscript.
The dotted border --> The marked rectangle The reconstruction trajectories …. --> Magnified portion of the reconstructed trajectory

Response：
The manuscript has been revised according to the reviewer's comments. The trajectories in Fig. 7 (a) are indeed designed ones, which used to show the entire powered descent. The trajectory reconstructed in this paper is only the part below the altitude of 6km as showed in Fig. 7 (b).
Please add: Altitude is given with respect to final landing site level.

Response：
The manuscript has been revised according to the reviewer's comments. "Altitude is given with respect to final landing site level." is added in the revised manuscript.