orbital dynamics – Daniel Estévez

Analysis of the CAMRAS Venus radar experiment

On March 22, CAMRAS performed a Venus radar experiment (or Earth-Venus-Earth bounce, as it is more commonly known in Amateur radio) in collaboration with Astropeiler Stockert, the Deep Space Exploration Society, and the Open Research Institute. The experiment was done in L-band, at 1299.5 MHz, using the 25 m Dwingeloo radiotelescope as transmitter and receiver and the Stockert 25 m telescope as a receiver. The experiment was done during the Venus conjunction, as this minimizes the distance between the Earth and Venus. The round-trip time to Venus was approximately 280 seconds. The radar waveform was a CW carrier with a duration of 278 seconds. It was transmitted a total of 4 times every 600 seconds. Thus each period was composed by:

278 second transmission
~2 second TX/RX guard time
278 second echo reception
~42 second wait

More transmissions were planned, including some spread-spectrum signals designed by the Open Research Institute. However, the transmitter started failing and they had to stop.

Update 2025-04-21: I have been informed that the spread-spectrum signal for this experiment was designed by CAMRAS. The waveform that the Open Research Institute is designing will potentially be used in future experiments.

CAMRAS has published an analysis of the recorded IQ data, showing successful echo detections with Dwingeloo and Stockert. There is an example Jupyter notebook that shows how to Doppler correct the echo and detect it with an FFT. All the recorded IQ data has been published.

In this post I will do my own analysis of the experiment. The goal is not to confirm the successful detection with an independent analysis, since I believe that the analysis published by CAMRAS is correct and leaves no doubt about this. It is to expand this analysis and to touch on other topics that this analysis has not covered:

Calculation of the Doppler. CAMRAS has published CSV files containing the expected Doppler at each receiver, but they have not published the code to calculate this. Here I will do all the relevant calculations with SPICE.
Doppler correction with the gr-satellites Doppler correction block, which performs linear interpolation of the Doppler frequency to calculate the frequency shift applied to each sample.
High-quality spectral analysis with a polyphase filterbank.
Try to estimate the Doppler spread and compare with some results in the literature.

Tianwen-1 second apoapsis raise

Some weeks ago I reported about an apoapsis raise manoeuvre done by Tianwen-1, the Chinese Mars orbiter. This has now happened again. Using state vectors from the telemetry decoded with the 20 m antenna in Bochum observatory by AMSAT-DL, we have detected an apoapsis raise manoeuvre done on 2025-01-08. This new apoapsis raise is much larger than the previous one. I have done the same kind of calculations as in the previous post, and also corrected a bug in my Keplerian elements plots (the periapsis and apoapsis passings were being paired incorrectly, which caused the SMA and eccentricity not to change in the plots I did in the previous post).

Tianwen-1 apoapsis raise

For a long time, AMSAT-DL has been using the 20 meter antenna in Bochum observatory to receive some telemetry from Tianwen-1, the Chinese Mars orbiter, almost daily. Since the telemetry includes the spacecraft’s state vectors, we can use this to monitor the spacecraft’s orbit. In 8 November 2021, Tianwen-1 entered its remote sensing orbit. This is an elliptical orbit with a period approximately 2/7 Mars sidereal days plus 170 seconds. This causes a ground track that is almost repeating, but drifts slowly to cover all the surface area of the planet.

I have been posting yearly updates about Tianwen-1’s orbit, the last of them this summer. In these updates, we can see that no manoeuvres have happened, and the changes in the Keplerian elements correspond to orbital perturbations caused by external forces. The orbit is in fact designed to cause the latitude of the periapsis to precess. In this way, all the surface of Mars can be scanned from low altitude.

Now we have some news. In the telemetry of the last few days we have detected that Tianwen-1 has raised its apoapsis radius from about 14134 km to 14489 km. All the data we have indicates that a propulsive burn has happened recently. In this post I give the details about this apoapsis raise manoeuvre.

2024’s update of Tianwen-1’s remote sensing orbit

Last year I wrote a post on July 23, which is the anniversary of Tiawen-1‘s launch. The post was essentially an updated plot of the orbital parameters of Tianwen-1’s remote sensing orbit. As I explained in that post, AMSAT-DL is using the 20 meter antenna in Bochum observatory to receive telemetry from Tianwen-1 almost every day (this can be followed in the YouTube livestream). Since Tianwen-1 includes its state vector (position and velocity with respect to Mars) in its telemetry, this allows us to monitor its orbit, which is of interest because no other public detailed information is available.

This year I completely forgot to do the same again for July 23, but I have remembered now. Here is the updated plot of the orbital parameters of Tianwen-1 since 8 November 2021, when the remote sensing orbit began. The plot includes data until 2 August 2024. During most of August, AMSAT-DL is not tracking Tianwen-1, since Mars has a very similar right ascension to STEREO-A, and tracking STEREO-A has priority. Tracking of Tianwen-1 will resume as the two objects drift apart in right ascension.

All the changes in the orbital parameters are due to perturbations by the Sun’s gravity and the oblateness of Mars, since as far as I know there have been no manoeuvres in this orbit. The main change in orbital parameters is a steady change in the latitude of the periapsis. The orbit is designed on purpose to exploit this effect. Over time, all the surface of Mars can be observed from a low altitude. This perturbation is related to a change in eccentricity, which is minimal when the periapsis is over the north pole and maximal when the periapsis is over the south pole.

Now it is quite apparent that there is also a slow but steady increase in inclination. This was not so evident last year, due to a sinusoidal perturbation that is also present, but now it is clear that the inclination has increased by about 0.05 deg since November 2021. It seems that this increase in inclination is related to a small increase in the semi-major axis.

The code for the updated plot can be found in this Jupyter notebook.

Tianwen-1 third anniversary

Today is the third anniversary of Tianwen-1, which was launched in 23 July 2020. During the first year of the mission I was tracking it with great detail and writing a lot of posts. A fundamental part of this work was the help of AMSAT-DL. Using its 20 metre antenna in Bochum, they tracked the spacecraft, decoded telemetry and provided live coverage of many of the key mission events in their Youtube livestream. At some point the reception of Tianwen-1’s telemetry at Bochum got completely automated, as we described in a paper in the GNU Radio Conference 2021 proceedings.

To this date, the reception continues in Bochum almost every day, when the dish is not busy with other tasks such as tracking STEREO-A. This means that we get good coverage of the spacecraft orbital data, via the state vectors transmitted in its telemetry.

To celebrate the anniversary, I have updated my plot of the orbital parameters, which I made back in March 2022. The plot covers all the remote sensing orbit, from when it started on 8 November 2021, until the present day. To my knowledge, no manoeuvres have happened in this time (perhaps small station-keeping burns would be unnoticed without more careful analysis), so the changes in the orbit are just due to perturbations by forces such as the Sun’s gravity and the oblateness of Mars.

The updated plot can be seen below. We see that the periapsis latitude changes at a steady rate of 0.598 deg/day. The remote sensing orbit was designed so that the periapsis precessed in this way, which allows the spacecraft to cover all the surface of Mars from a low altitude in 301 days. The surface has now been covered twice, since the periapsis has moved from near the north pole to the south pole and back again to the north pole.

There is also an interesting change in eccentricity, which seems to be correlated with the latitude of the periapsis. The eccentricity is largest when the periapsis is over the south pole. In this case, the altitude of the periapsis decreases by 60 km, compared to when the periapsis is over the north pole. The inclination has remained mostly steady, although there seems to be a small perturbation with an amplitude of 0.1 deg.

The updated Jupyter notebook in which this plot was made can be found here.

Mars Express 20th anniversary livestream

On June 2, ESA celebrated the 20th anniversary of the launch of Mars Express (MEX) by livestreaming images of Mars from the VMC camera in a Youtube livestream. They set things up so that an image was taken by the camera approximately every 50 seconds, downlinked in the X-band telemetry to the Cebreros groundstation, which was tracking the spacecraft, and then sent to the Youtube. The total latency, according to the image timestamps that were shown in Youtube was around 17 minutes, which is quite good, since most of that latency was the 16 minutes and 45 seconds of one-way light time from Mars to Earth.

The livestream was accompanied by commentary from Simon Wood and Jorge Hernández Bernal. One of the things that got my attention during the livestream was the mention that to make the livestream work, the VMC camera should be pointing to Mars and the high-gain antenna should be pointing to Earth. This could only be done during part of Mars Express orbit, and in fact reduced the amount of sunlight hitting the solar panels, so it could not be done for too long.

This gave me the idea to use the Mars Express SPICE kernels to understand better how the geometry looked like. This is also a good excuse to show how to use SPICE.

More QO-100 orbit determination

In a previous post, I showed my orbit determination experiments of the GEO satellite Es’hail 2 using the beacons transmitted from Bochum (Germany) through the QO-100 amateur radio transponder on-board this satellite. By measuring the phase difference of the BPSK and 8APSK beacons, which are spaced apart by 245 kHz in the transponder, we can compute the three-way range-rate between the transmitter at Bochum and my receiver in Spain. This data can then be used for orbit determination with GMAT.

I have continued collection more data for these experiments, so this post is an update on the results.

QO-100 orbit determination

In a previous post, I showed my experiment about measuring the phase difference of the 8APSK and BPSK beacons of the QO-100 NB transponder. The main goal of this experiment was to use this data to do orbit determination with GMAT. Over the last week I have continued these experiments and already have started to perform some orbit determination in GMAT.

Here I give an update about several aspects of the experiment, and show how I am setting up the orbit determination.

An update about Tianwen-1’s remote sensing orbit

Tianwen-1, the Chinese Mars orbiter, entered its remote sensing orbit on November 8 2021. In a previous post, I gave an overview of the orbit using one month of state vector data collected from the spacecraft’s telemetry by AMSAT-DL using the 20 m antenna at Bochum observatory. AMSAT-DL has continued receiving telemetry almost every day, so in this post we can now look at nearly 4 months of data for the remote sensing orbit.

This orbit is a polar elliptical orbit with 86 deg inclination, a periapsis altitude of 275 km and an apoapsis radius of 14140 km. The orbital period is approximately 2/7 Mars sidereal days plus 170 seconds. This makes the ground track drift slowly towards the west, allowing the spacecraft to scan all the planet’s surface. Additionally, due to orbit perturbations, the argument of periapsis (and hence its latitude) keeps slowly changing with time. This makes possible to scan all of Mars from a low altitude.

One month of Tianwen-1 remote sensing orbit

In a previous post, I described the remote sensing orbit into which Tianwen-1 had moved on November 8. Now it has been in this orbit for more than one month, and AMSAT-DL has been collecting telemetry almost daily with the 20 metre antenna at Bochum obseratory. Therefore, it is a good moment to review the state vector data and look at how the orbit has evolved with time.