<p>a &quot;tentative answer&quot;.</p>
<p>I did not find that the accelerometer was installed this satellite. On the contrary, I found a number of articles on improving the accuracy of the satellite position with mathematical methods. For example string &quot;Ballistic and navigation support for “Spektr-R” spacecraft&quot; for googling.</p>
<p>1/
1.In russian</p>
<blockquote>
<p>The paper describes developed models and techniques for orbit determination and prediction of a spacecraft, the motion of which undergoes significant perturbations due to variable solar radiation pressure and occasional firings of stabilization system thrusters. To compare the orbit of the spacecraft
has been determined and predicted by several ways using real tracking and on-board data.</p>
</blockquote>
<blockquote>
<p>Для получения дополнительной информации о возмущениях от разгрузок двигателей-маховиков и переменного светового давления будем использовать бортовые измерения, в том числе данные звездных датчиков об ориентации КА в пространстве, параметры работы двигателей стабилизации, а также скорости вращения двигателей маховиков.</p>
<p>To obtain additional information about the disturbances from the unloading of the flywheel motors and variable light pressure, we will use onboard measurements, including the data of star sensors on the spacecraft orientation in space, the operation parameters of the stabilization motors, as well as the rotation speed of the flywheel motors.</p>
</blockquote>
<p><a href="https://lppm3.ru/files/journal/XXX/MathMontXXX-Borovin.pdf" rel="nofollow noreferrer">https://lppm3.ru/files/journal/XXX/MathMontXXX-Borovin.pdf</a></p>
<ol start="2">
<li>In English: &quot;DETERMINATION AND PREDICTION OF ORBITAL PARAMETERS OF THE
RADIOASTRON MISSION&quot;</li>
</ol>
<blockquote>
<p>Direct solar radiation pressure (SRP) and operation of stabilization thrusters during unloadings of reaction wheels are the major uncertainties that affect the Radioastron. Both effects have significant impact on the orbit and cannot be ignored since accurate orbit is vital for correct processing of interferometric observations. This paper introduces developed direct SRP model, which allows to calculate both acceleration and torque due to impacting solar radiation. <strong>The spacecraft is not equipped with accelerometers</strong>, but a telemetry of the reaction wheels can be used to measure perturbing torque and to obtain additional information about unknown parameters of the SRP model. The paper shows how the SRP model along with consideration of unloadings significantly improves the accuracy of the orbit.</p>
</blockquote>
<p><a href="https://issfd.org/ISSFD_2014/ISSFD24_Paper_S18-5_zakhvatkin.pdf" rel="nofollow noreferrer">https://issfd.org/ISSFD_2014/ISSFD24_Paper_S18-5_zakhvatkin.pdf</a></p>
<ol start="3">
<li>Determination and Prediction of Orbital Parameters of the Radioastron Mission</li>
</ol>
<blockquote>
<p>Summary
Adjustable Radioastron SRP model was developed and tested.
Parameters of the SRP model was estimated by using both motion of the center of mass and motion around the center of mass.
Determined orbits are successfully used for correlation of the Radioastron observations.
An unloading prediction approach, important for future Sun-Earth L2 missions (Spectr-R,‘Millimetron) based on the same platform, was tested on the Radioastron data</p>
</blockquote>
<p><a href="http://www.kiam1.rssi.ru/pubs/20140509_ISSFD24_Zakhvatkin.pdf" rel="nofollow noreferrer">http://www.kiam1.rssi.ru/pubs/20140509_ISSFD24_Zakhvatkin.pdf</a></p>
<ol start="4">
<li>Navigation Support for the RadioAstron Mission</li>
</ol>
<blockquote>
<p>A developed method of determination of orbital parameters allows one to estimate, along with orbit elements, some additional parameters that characterize solar radiation pressure and perturbing accelerations due to unloadings of reactiion wheels. A parameterized model of perturbing action of solar radiation pressure on the spacecraft motion is described (this model takes into account the shape, reflecting properties of surfaces, and spacecraft attitude). Some orbit determination results are presented obtained by the joint processing of radio measurements of slant range and Doppler, laser range measurements used to calibrate the radio measurements, optical observations of right ascension and declination, and telemetry data on space craft thrusters' firings during an unloading of reaction wheels</p>
<p>This fact makes the following demands to the accuracy of the determination of spacecraft motion parameters: at position Δr = ±600 m; at velocity = ±2 cm/s; and at acceleration Δw = ±10–8 m/s2</p>
</blockquote>
<p><a href="http://www.asc.rssi.ru/radioastron/publications/articles/cr_2014,52,342.pdf" rel="nofollow noreferrer">http://www.asc.rssi.ru/radioastron/publications/articles/cr_2014,52,342.pdf</a></p>

CC BY-SA 4.0
2021-07-05T11:41:09.940Z
Wow, you found an authoritative source and definitive answer, fantastic!
uhoh
CC BY-SA 4.0
2021-07-05T11:24:11.383Z
2021-07-05T11:24:11.383Z
A. Rumlin
<p><a href="https://astronomy.stackexchange.com/a/43537/7982">This answer to <em>Why is space-based VLBI scattering sub-structure &quot;Hopefully, a new promising tool to reconstruct the true image of observed background target(s)&quot;?</em></a> summarizes the contribution of the RadioAstron mission, a VLBI collaboration of radio telescopes using the <a href="https://en.wikipedia.org/wiki/Spektr-R#Observing_techniques" rel="nofollow noreferrer">Spectr-R</a> space-based 10 m dish in high Earth orbit to produce &quot;very-VLBI&quot; observations.</p>
<p>Figure 2 of Gwinn et al. (2014): <a href="https://arxiv.org/abs/1409.0530" rel="nofollow noreferrer">Discovery of Substructure in the Scatter-Broadened Image of Sgr A*</a> shown below shows projected baseline distances out past 260,000 km!</p>
<p>What's notably different in space-based VLBI is that some of the radio telescopes are not rotating with the Earth but basically doing their own thing, flying though space unattached to a (mostly) rigid planet.</p>
<p>For orbits at this distance it's absolutely necessary to consider gravity from the Earth, Moon and Sun to reconstruct even short segments of trajectory. Luckily present day ephemerides make this possible, and combining those with fringe optimization algorithms (<a href="https://physics.stackexchange.com/a/630432/83380">example</a>) one can get a good idea how to build a baseline trajectory for an observation.</p>
<p>However, large spacecraft are also subject to non-gravitational forces that also affect their trajectory.</p>
<p>An <em>accelerometer</em> will not register gravitational orbital perturbations as it's subject to the same gravity as the rest of the spacecraft, but things like photon pressure from the Sun which is quite difficult to model accurately can in principle be directly measured in real time with a sufficiently sensitive accelerometer.</p>
<p>From <a href="http://www.asc.rssi.ru/radioastron/" rel="nofollow noreferrer">http://www.asc.rssi.ru/radioastron/</a> I found <a href="http://www.asc.rssi.ru/radioastron/documents/memo/memo5.htm" rel="nofollow noreferrer">On the optimization of the RadioAstron mission by using advanced observing methods at ground radio telescopes and tracking stations, and the advantages of using on-board H-maser frequency standard and on-board accelerometer</a> (Astro Space Center, Moscow, June 2003). <em>5. High accuracy orbit determination and anomalous acceleration</em> nicely describes the fringe-fitting technique and concerns about residual accelerations due to both</p>
<ul>
<li>solar wind pressure</li>
<li>solar photon pressure</li>
</ul>
<p>Note that a residual error of only 2 millimeters over the coherent integration time (typically of order 1000 seconds) results in a 10% loss of fringe visibility!</p>
<blockquote>
<ol start="5">
<li>High accuracy orbit determination and anomalous acceleration</li>
</ol>
<p>[...]<strong>SuperSTAR accelerometer (AM) recently developed and tested by ONERA provides the accuracy of <sup>-10</sup> m/s<sup>2</sup> along all three axis of the spacecraft [7]. The evaluations presented above have shown that solar pressure, solar wind (variable in strength and direction) especially inside the magnetosphere, and evaporation of gas from the spacecraft will cause SRT acceleration in the range of 10<sup>-10</sup> - 10<sup>-8</sup> m/s<sup>2</sup>.</strong></p>
<p>Conclusion: AM will provide a possibility to reduce considerably the effects of errors in SRT acceleration thus increasing coherent integration time from several minutes to several hours when new reference-sources observations could be done. AM will also help to decrease time of fringe search at the correlator because of smaller values in uncertainty of delay and fringe rate.</p>
<ol start="7">
<li>Kellerman, K.I., Vermeulen, R.C., Zensus, J.A., &amp; Cohen, M.H., AJ, 115, 1295-1318, 1998.</li>
</ol>
</blockquote>
<p>and later</p>
<blockquote>
<ol start="8">
<li>Conclusion</li>
</ol>
<p>On-board H-maser frequency standard and high accuracy on-board accelerometer included into the scientific payload of RadioAstron mission will permit us to increase the coherent integration time up to 5-30 minutes at the correlator before fringe detection. This will be resulted in 2-5 times improvement in sensitivity by increasing the coherence time up to 5-30 minutes. To reach these potential figures we propose advanced observing methods using the measurements of the atmospheric path delay variations by the monitoring of 22 GHz water vapor line emission along a line of sight to the observing source  (WLM) and/or by using reference radio telescope located at high mountain. Additional gain in sensitivity can be obtained by applying self-calibration in fringe-fitting procedure during image reconstruction.</p>
<p>As it is known from regular ground VLBI observations, maximum coherence time at 22 GHz is about 80 seconds. WLM observing technique or/and usage of reference radio telescope on high  mountain (HMRT) will increase the integration time by 2-3 times. On-board H-maser frequency standard will also provide the possibility to increase the integration time by 2-3 times. <strong>On-board accelerometer will provide necessary accuracy of orbit determination to realize potential maximum integration time by 2-3 and to simplify fringe search at the correlator.</strong></p>
</blockquote>
<h3>Here it is, my question:</h3>
<p>This is all written in 2003 and in future tense. Was the accelerometer actually used in data analysis throughout Spektr-R's long-lived VLBI mission, or were non-gravitational acceleration models eventually used which were likely to be smoother than noisy accelerometer data?</p>

CC BY-SA 4.0
2021-05-31T12:47:25.330Z
I did not find that the accelerometer was installed this satellite. On the contrary, I found a number of articles on improving the accuracy of the satellite position with mathematical methods.
A. Rumlin
CC BY-SA 4.0
2021-05-31T12:56:45.877Z
@A.Rumlin thank you for looking into it! It would have to be an extremely sensitive accelerometer with very very low drift/offset. I asked the question because it seems to be quite difficult to do in practice.
uhoh
CC BY-SA 4.0
2021-05-31T18:33:57.673Z
String "Ballistic and navigation support for “Spektr-R” spacecraft" for googling.
A. Rumlin
CC BY-SA 4.0
2021-06-27T08:07:35.493Z
@A.Rumlin why not write that up as a "tentative answer"? There doesn't seem to be much else available, and I think in this case, considering the challenges of a drift-free accelerometer it seems likely that they didn't. GAIA didn't either.
uhoh
CC BY-SA 4.0
2021-07-05T11:26:03.560Z
added quote "The spacecraft is not equipped with accelerometers"
A. Rumlin
<radio-astronomy><space-telescope><radio-telescope><vlbi>
Did the Spectr-R space-based radio telescope use on-board accelerometer to measure non-gravitational acceleration for baseline correction?
uhoh
# Did the Spectr-R space-based radio telescope use on-board accelerometer to measure non-gravitational acceleration for baseline correction?

(Asked by: username_0 on 2021-04-25)

[This answer to *Why is space-based VLBI scattering sub-structure "Hopefully, a new promising tool to reconstruct the true image of observed background target(s)"?*](https://astronomy.stackexchange.com/a/43537/7982) summarizes the contribution of the RadioAstron mission, a VLBI collaboration of radio telescopes using the [Spectr-R](https://en.wikipedia.org/wiki/Spektr-R#Observing_techniques) space-based 10 m dish in high Earth orbit to produce "very-VLBI" observations.

Figure 2 of Gwinn et al. (2014): [Discovery of Substructure in the Scatter-Broadened Image of Sgr A\*](https://arxiv.org/abs/1409.0530) shown below shows projected baseline distances out past 260,000 km!

What's notably different in space-based VLBI is that some of the radio telescopes are not rotating with the Earth but basically doing their own thing, flying though space unattached to a (mostly) rigid planet.

For orbits at this distance it's absolutely necessary to consider gravity from the Earth, Moon and Sun to reconstruct even short segments of trajectory. Luckily present day ephemerides make this possible, and combining those with fringe optimization algorithms ([example](https://physics.stackexchange.com/a/630432/83380)) one can get a good idea how to build a baseline trajectory for an observation.

However, large spacecraft are also subject to non-gravitational forces that also affect their trajectory.

An *accelerometer* will not register gravitational orbital perturbations as it's subject to the same gravity as the rest of the spacecraft, but things like photon pressure from the Sun which is quite difficult to model accurately can in principle be directly measured in real time with a sufficiently sensitive accelerometer.

From <http://www.asc.rssi.ru/radioastron/> I found [On the optimization of the RadioAstron mission by using advanced observing methods at ground radio telescopes and tracking stations, and the advantages of using on-board H-maser frequency standard and on-board accelerometer](http://www.asc.rssi.ru/radioastron/documents/memo/memo5.htm) (Astro Space Center, Moscow, June 2003). *5. High accuracy orbit determination and anomalous acceleration* nicely describes the fringe-fitting technique and concerns about residual accelerations due to both

* solar wind pressure
* solar photon pressure

Note that a residual error of only 2 millimeters over the coherent integration time (typically of order 1000 seconds) results in a 10% loss of fringe visibility!

> 5. High accuracy orbit determination and anomalous acceleration
>
> [...]**SuperSTAR accelerometer (AM) recently developed and tested by ONERA provides the accuracy of -10 m/s2 along all three axis of the spacecraft [7]. The evaluations presented above have shown that solar pressure, solar wind (variable in strength and direction) especially inside the magnetosphere, and evaporation of gas from the spacecraft will cause SRT acceleration in the range of 10-10 - 10-8 m/s2.**
>
> Conclusion: AM will provide a possibility to reduce considerably the effects of errors in SRT acceleration thus increasing coherent integration time from several minutes to several hours when new reference-sources observations could be done. AM will also help to decrease time of fringe search at the correlator because of smaller values in uncertainty of delay and fringe rate.
>
> 7. Kellerman, K.I., Vermeulen, R.C., Zensus, J.A., & Cohen, M.H., AJ, 115, 1295-1318, 1998.

and later

> 8. Conclusion
>
> On-board H-maser frequency standard and high accuracy on-board accelerometer included into the scientific payload of RadioAstron mission will permit us to increase the coherent integration time up to 5-30 minutes at the correlator before fringe detection. This will be resulted in 2-5 times improvement in sensitivity by increasing the coherence time up to 5-30 minutes. To reach these potential figures we propose advanced observing methods using the measurements of the atmospheric path delay variations by the monitoring of 22 GHz water vapor line emission along a line of sight to the observing source (WLM) and/or by using reference radio telescope located at high mountain. Additional gain in sensitivity can be obtained by applying self-calibration in fringe-fitting procedure during image reconstruction.
>
> As it is known from regular ground VLBI observations, maximum coherence time at 22 GHz is about 80 seconds. WLM observing technique or/and usage of reference radio telescope on high mountain (HMRT) will increase the integration time by 2-3 times. On-board H-maser frequency standard will also provide the possibility to increase the integration time by 2-3 times. **On-board accelerometer will provide necessary accuracy of orbit determination to realize potential maximum integration time by 2-3 and to simplify fringe search at the correlator.**

### Here it is, my question:

This is all written in 2003 and in future tense. Was the accelerometer actually used in data analysis throughout Spektr-R's long-lived VLBI mission, or were non-gravitational acceleration models eventually used which were likely to be smoother than noisy accelerometer data?

**Tags:** radio-astronomy, space-telescope, radio-telescope, vlbi

> **Comments:**
> **username_1**: I did not find that the accelerometer was installed this satellite. On the contrary, I found a number of articles on improving the accuracy of the satellite position with mathematical methods.  
> **username_0**: @A.username_1 thank you for looking into it! It would have to be an extremely sensitive accelerometer with very very low drift/offset. I asked the question because it seems to be quite difficult to do in practice.  
> **username_1**: String "Ballistic and navigation support for “Spektr-R” spacecraft" for googling.  
> **username_0**: @A.username_1 why not write that up as a "tentative answer"? There doesn't seem to be much else available, and I think in this case, considering the challenges of a drift-free accelerometer it seems likely that they didn't. GAIA didn't either.  
> **username_1**: added quote "The spacecraft is not equipped with accelerometers"  

---

## 1 answers

### Answer by username_1 on 2021-07-05. Score: 1 | Accepted answer

a "tentative answer".

I did not find that the accelerometer was installed this satellite. On the contrary, I found a number of articles on improving the accuracy of the satellite position with mathematical methods. For example string "Ballistic and navigation support for “Spektr-R” spacecraft" for googling.

1/
1.In russian

> The paper describes developed models and techniques for orbit determination and prediction of a spacecraft, the motion of which undergoes significant perturbations due to variable solar radiation pressure and occasional firings of stabilization system thrusters. To compare the orbit of the spacecraft
> has been determined and predicted by several ways using real tracking and on-board data.

> Для получения дополнительной информации о возмущениях от разгрузок двигателей-маховиков и переменного светового давления будем использовать бортовые измерения, в том числе данные звездных датчиков об ориентации КА в пространстве, параметры работы двигателей стабилизации, а также скорости вращения двигателей маховиков.
>
> To obtain additional information about the disturbances from the unloading of the flywheel motors and variable light pressure, we will use onboard measurements, including the data of star sensors on the spacecraft orientation in space, the operation parameters of the stabilization motors, as well as the rotation speed of the flywheel motors.

<https://lppm3.ru/files/journal/XXX/MathMontXXX-Borovin.pdf>

2. In English: "DETERMINATION AND PREDICTION OF ORBITAL PARAMETERS OF THE
   RADIOASTRON MISSION"

> Direct solar radiation pressure (SRP) and operation of stabilization thrusters during unloadings of reaction wheels are the major uncertainties that affect the Radioastron. Both effects have significant impact on the orbit and cannot be ignored since accurate orbit is vital for correct processing of interferometric observations. This paper introduces developed direct SRP model, which allows to calculate both acceleration and torque due to impacting solar radiation. **The spacecraft is not equipped with accelerometers**, but a telemetry of the reaction wheels can be used to measure perturbing torque and to obtain additional information about unknown parameters of the SRP model. The paper shows how the SRP model along with consideration of unloadings significantly improves the accuracy of the orbit.

<https://issfd.org/ISSFD_2014/ISSFD24_Paper_S18-5_zakhvatkin.pdf>

3. Determination and Prediction of Orbital Parameters of the Radioastron Mission

> Summary
> Adjustable Radioastron SRP model was developed and tested.
> Parameters of the SRP model was estimated by using both motion of the center of mass and motion around the center of mass.
> Determined orbits are successfully used for correlation of the Radioastron observations.
> An unloading prediction approach, important for future Sun-Earth L2 missions (Spectr-R,‘Millimetron) based on the same platform, was tested on the Radioastron data

<http://www.kiam1.rssi.ru/pubs/20140509_ISSFD24_Zakhvatkin.pdf>

4. Navigation Support for the RadioAstron Mission

> A developed method of determination of orbital parameters allows one to estimate, along with orbit elements, some additional parameters that characterize solar radiation pressure and perturbing accelerations due to unloadings of reactiion wheels. A parameterized model of perturbing action of solar radiation pressure on the spacecraft motion is described (this model takes into account the shape, reflecting properties of surfaces, and spacecraft attitude). Some orbit determination results are presented obtained by the joint processing of radio measurements of slant range and Doppler, laser range measurements used to calibrate the radio measurements, optical observations of right ascension and declination, and telemetry data on space craft thrusters' firings during an unloading of reaction wheels
>
> This fact makes the following demands to the accuracy of the determination of spacecraft motion parameters: at position Δr = ±600 m; at velocity = ±2 cm/s; and at acceleration Δw = ±10–8 m/s2

<http://www.asc.rssi.ru/radioastron/publications/articles/cr_2014,52,342.pdf>

> **Comments:**
> **username_0**: Wow, you found an authoritative source and definitive answer, fantastic!  

---

