A Method for Measuring Gravitational Potential of Satellite’s Orbit Using Frequency Signal Transfer Technique between Satellites

Round 1

Reviewer 1 Report

They introduce an approach for the direct measurement of the gravitational potential (GP) along the trajectory of a satellite, with a specific focus on Low-Earth Orbit (LEO) satellites. An LEO satellite communicates with several Geosynchronous Equatorial Orbit (GEO) satellites via frequency signal links.The results indicated that the accuracy of the GP measurements along the LEO satellite’s trajectory primarily depends on the precision of the onboard atomic clocks. Supposing optical atomic clocks attain an instability level of 1 × 10−17τ−1/2 (τ in seconds), they determined the GP distribution covered by the LEO satellite’s trajectories with 30-day observations. Then we determined a gravitational field at the centimeter level based on the GP distribution. The GP data derived from the trajectory of an LEO satellite can be utilized to establish temporal gravitational fields, which have broad applications in different disciplines.

This article is very interesting and the subject matter is very novel.This research is very meaningful, but there are still some small problems, and the quality of the article will be greatly improved after taking these details into account.

1.It is suggested that the last two paragraphs of the introduction be merged and that the innovations of the manuscript be condensed.

2.The picture quality of the manuscript is good, but the content of the title is too bloated. It is recommended to present the specific principles in the original manuscript, not in the title. Please revise the whole manuscript.

3.Whether the figures and tables on page 13 can be reordered, the connection between the upper and lower paragraphs is really unacceptable.

4.The English style of the whole manuscript is too Chinglish, and it is suggested to modify the language style.

Language style moderate modification.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The article is interesting and engagingly written. It summarizes a large volume of work - calculations and tests.

This is a continuation of works that were published in 2016-2022.

For the whole matter of determining the gravitational potential from changes in the frequency of atomic clocks, I consider fundamental determination of the exact (1 cm) position of both LEO and GEO satellites. Especially with GEO satellites today, determination is problematic their path to 1 cm, according to (*) it is to approx. 1 dm. But it is likely that when optical can be developed atomic clock operating in satellite conditions, that there will already be a problem with determining the path of GEO satellites to 1 cm also solved. Please modify line 279 accordingly.

You work with the difference in gravitational potential on different tracks or heights. You take into account the so-called attenuation potential with height ? I don't see it there.

The information at line 411: "level of 10~20 cm" does not follow from the results, nor is there a citation. Where did she come from?

Minor notes:

Table 1 is not cited in the text.

Table 2 position error - 10-10 is incorrectly stated

line 290 ionospheric error is very variable and very difficult to measure during the maximum of the solar cycle model with an accuracy of 10-19

Table 3, table 4: explain the abbreviation SD or describe it in the table "standard deviation"

Figure 8 b: maximal or minimal values are not visible at all

Abbreviations: missing SD standard deviation

References: out of 57 citations, I identify 6 self-citations. I consider this adequate for publication of ongoing research.

(*)

Xingxing Li , Yiting Zhu , Kai Zheng , Yongqiang Yuan , Gege Liu , Yun Xiong: Precise orbit and clock products of Galileo, BDS and QZSS from MGEX since 2018: comparison and PPP validation. Remote Sensing, 12(9), 1415, doi: 10.3390/rs12091415

Pengli Shen , Fang Cheng , Xiaochun Lu , Xia Xiao , Yulong Ge: An investigation of precise orbit and clock products for BDS-3 from different analysis centers, Sensors, 21(5), 1596, doi: 10.3390/s21051596

Author Response

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Reviewer 3 Report

In this manuscript, authors introduced a method to calculate the gravitational potential on low Earth orbit satellite orbits using precise clocks and frequency signal transmission between satellites. By the high-precision clock comparisons between low-Earth orbit satellites and geosynchronous equatorial orbit satellites, and numerical simulation experiments, authors demonstrated that clock data can be used to determine gravitational potentials on satellite orbit and Earth's gravity field. Based on analysis of this work, the gravitational potential data from satellites in near-Earth orbits can be used to establish a temporal gravity field, which has wide applications in various disciplines. I recommend that this paper be published once the handful of minor comments below are addressed.

1) In equation 2, although the first-order Doppler effect is eliminated, the higher-order Doppler effects still remain. It should be discussed or assessed whether these higher-order Doppler effects will affect the determination of gravitational potentials.

2) The tidal effects on satellite clocks quadratically increase with the distances between satellite to Earth’s mass center. For clocks on the geosynchronous equatorial orbit satellites, tidal effects are much significantly greater than 10^{-17} and should be considered with greater attention in the simulation experiments (sec.3).

3)  As ϕ has been used for gravitational potentials, it would be prudent to change the white noise component ϕ in equation (8) to a different variable.

Author Response

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Author Response File: Author Response.pdf