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Pair, three-of-a-kind, two pair? The odds for the next gravity mission

By 3 November 2021January 30th, 2024Space geodesy

Future gravity missions

Let’s make a short break from the “Focusing efforts in the right direction” series (we’ll come back to eigenvectors and eigenvalues soon), and talk about another burning topic: the future of gravity missions.

The best hand in poker

In a scene of the excellent Casino Royale, Vesper Lynd and James Bond are on a train to Montenegro, on their way to beat Le Chiffre at a poker game (and consequently save Queen and Country). They’re sipping a glass of fine red wine, and she wonders out of perplexity: “So there is a plan? I got the impression that we were risking millions of dollars on a game of luck”. 15 millions exactly. Quite nothing actually. Let’s raise the stakes by 10 to 40 times and we’re ready to discuss the next gravity mission. While devising the strategy, Bond tells Vesper: “In poker, you never play your hand, you play the man across from you”. And Vesper to answer: “So what would be what you call bluffing?”. Ensues a suspenseful poker game, until 007 wins it all. So, supposing the best hand wins, and bluff doesn’t work out, what are the odds for the next gravity constellation? A pair of satellites? Three-of-a-kind? Two pairs?

Pair, three-of-a-kind, two pair?

We actually have good clues about the next scenarios, since we were involved in the simulations. Stellar Space Studies and CNES have been working together on different concepts. Let’s share with the main 4 scenarios involved:

Next gravity mission scenarios (Credits: CNES)

  • Top left: The Single Polar Pair. This is the historical GRACE/GRACE-FO concept. It works well, but the lack of measurements in the East-West direction is responsible for the North-South noisy stripes in the solutions.
  • Top right: The Radial Constellation. This is made of one LEO satellite, plus several MEO satellites (7000 km). This concept also has additional advantages for geodesy, namely the determination of the system of reference.
  • Bottom left: The Pendulum. This is made of is one polar satellite (or one polar pair), plus an additional satellite with a shift in right ascension of ascending node and in anomaly. It has the advantage of providing East-West measurements, and solving the main weakness of GRACE. It has technical challenges though, especially in terms of precise pointing and attitude.
  • Bottom right: The Double Pair, a.k.a BENDER. This is made of one standard polar pair and one inclined pair (70°). This is a master concept, the most robust and the most efficient at first glance. But also the more costly.

Immediate improvement by better geometry

The radial constellation was quickly ruled out by the performance in gravity field restitution. The pendulum and the BENDER are very interesting because they solve the geometric problem of the single polar pair. With the across-track link provided by the pendulum or the 70° inclination of the second pair, you get access to the missing East-West information. This solves the vertical stripes headache that we’ve been experiencing with GRACE and GRACE Follow-On since the start (and the reason for all our tricks on the SVD inversion, which are a perfect example of “innovation by necessity”). So here is the improvement of the error structure in simulation when we go from a polar pair to a two-satellite pendulum.


Map of errors in a GRACE-type configuration (polar pair)

Map of errors in a pendulum-type configuration

We immediately see that the geometric structure of errors has changed. The presence of East-West information cleans the vertical stripes. With such a good geometry in the observations, there is no more need for eigenvalues or eigenvectors (nor filtering). You might say: why didn’t we do it at first? The technology for a link with changing attitude in a pendulum configuration is much harder to achieve than the one for a straight constant North-South link in the polar pair. But as time goes by, so does progress. We will see what the future holds.

Shaken, not stirred

We only showed you a very brief example of the simulations in this article, just to arouse your curiosity. The simulations are very voluminous and complex because of the number of parameters involved (the level of noise on each instrument (KBR, LRI, accelerometers, GPS, attitude), the colored noise model applied, the altitude(s) of the satellites, the distance between the satellites, the angles in the pendulum configuration, and so on and so forth). Even Le Chiffre could not figure all the probabilities by mental calculation. So, which hand is going to win? We can’t say for sure, but we might ultimately get a two-pair by merging the hands of several players (ESA and NASA). Meanwhile, let’s have a drink. A dry Martini. Wait. Three measures of Gordon’s, one of vodka, half a measure of Kina Lillet! Shaken, not stirred.