# Source for up-to-date values of Mars' standard gravitational parameter

Wikipedia currently gives the standard gravitational parameter of Mars as:

$$GM_{Mars} = 4.2828(9) *10^{13} (m^3/s^2)$$

The (9) is the uncertainty of the last digit, so it works out to about 210ppm (parts per million) which is astronomically large (pardon the pun).

note: the Standard Gravitational Parameter of a body is the product of the gravitational constant G and the mass M of the body. Orbital data of satellites (natural and artificial) depends on the product of the two, so it can both be measured to higher precision (accuracy?) and it's actually just the thing you need to calculate the next mission's trajectory.

With all of the orbiting satellites and landers, I'm guessing there are updated values with more digits. This answer is helpful, but while the linked page for solar system satellites ssd.jpl.nasa.gov/?sat_phys_par lists GM, a similar page for planets ssd.jpl.nasa.gov/?planet_phys_par lists M in kg:

$$M_{Mars} = 0.641693 ± 0.000064 *10^{24} (kg)$$

That value still has an uncertainty of 100ppm, and if one tries to recover GM by multiplying by Gravitational constant G, the uncertainty there is still also high - about 47ppm.

My question: What is a good source for the most up-to-date value of Mars' standard gravitational parameter which also gives the experimental uncertainty of the value?

Bonus: The same Wikipedia article gives a value for pluto of:

$$GM_{Pluto} = 8.71(9) *10^{11} (m^3/s^2)$$

which has an uncertainty of 1%! (10,000ppm). Has the recent New Horizons fly-by trajectory and extended imaging been enough to improve on this value?

The most up-to-date is from the work in this paper, due to be published in July 2016. The actual numbers can be found in this large file, for which the number you seek is the second number in the file, and its uncertainty is the third number in the file. (The rest of the numbers are the higher order terms of the gravity field. You can find a detailed description here.)

Here are those numbers, copied and pasted from the file, in units of $\mathrm{{km}^3/s^2}$:

4.2828372854187757e+04, 1.6202815226760665e-05


I would write that a little more accessibly as $42828.372854(16)\,\mathrm{{km}^3/s^2}$, where the two digits in parentheses is the $1\sigma$ uncertainty in the last two digits of the value. Note that if you need that many digits in GM, then you also need a higher order gravity field to get the real answer.

The GM of Pluto is best determined by observations of it and its moons over long periods of time. The value I found in this recent paper is $869.6\pm 1.8\,\mathrm{{km}^3/s^2}$ (where the error is about $0.2\%$). New Horizons may have improved that some, by virtue of better locating Pluto and its moons. But I suspect not by much.

• OK another 'Yippee! Excellent!' but even better. 2016 - indeed the best possible "Source for up-to-date values of Mars' standard gravitational parameter" Thanks for bringing it home! – uhoh May 3 '16 at 15:35
• +1 for "if you need that many digits, then you also need a higher order gravity field". – Ilmari Karonen May 3 '16 at 18:28

Mars has had a number of studies to determine the gravitational constant. The best paper that I was able to find dates to 2001, using MGS data, and estimates Mars's GM to be 42828.371901 uncertainty .000074 km3/s2, which was calculated by two independent papers at the same time. I show that to be about 6 ppb, much closer to the Standard Gravitational Parameter's accuracy from Earth. This is about what the accuracy of the fraction of Mars/Sun's mass is shown from this page from NASA, which shows an accuracy of about 30 ppb. So I would use this number, with an assumed accuracy on the order of 10 ppb.

I found an even better source, using 2011 data, that lists the GM as GM =4.2828372 x1013 m3 s-2. Assuming the last digit is the uncertainty, the accuracy is about 20 ppb.

As for Pluto, I suspect a small improvement will be made from New Horizons but it really takes orbital data to get accurate GM calculations. The flybys of Mars gave an accuracy on the order of 10 ppm, which I suspect will not be achievable with Pluto due to the already extreme distance and very high speed flyby, but a small improvement is likely.

• Yippee! Excellent! The very small uncertainty makes a lot of sense, considering the number and duration of successful orbiter missions to Mars. Thank you for your persistence and your rationalization that there should be a number out there with similar precision to Earth due to the extensive data available. – uhoh May 3 '16 at 13:17
• Found a better source BTW. Now, off to correct Wikipedia;-) – PearsonArtPhoto May 3 '16 at 13:18
• Great - though technically it doesn't pass the "... which also gives the experimental uncertainty of the value?" part of the My question: summary. My high-school physics teacher (a zillion years ago) was a real stickler for the inclusion of both units and uncertainty (estimate at least) for any experimental value reported. To this day I am allergic to values that don't have both explicitly next to the value. So I'll stick with 2001 here also until we can find it. – uhoh May 3 '16 at 13:25
• I think there's a linked source on the later article that you could dig in to if you want. I've spent enough time on this issue already... – PearsonArtPhoto May 3 '16 at 13:31
• above and beyond, thanks! I just didn't want to loose the 2001 link from your answer. – uhoh May 3 '16 at 13:42