# Did the Mars rovers actually confirm the gravity of Mars?

For years the theoretical calculated gravity of Mars has proliferated science texts and Internet documentation - but did the rover actually do a test to confirm the theoretical gravity is truly equal to the actual measured gravity?

• Just on principle the landers would have had trouble landing if Mars' gravity was far from its expected value. So in a way the survival of the various rovers proves the number is approximately correct. (Does this answer the question?) – Andy Apr 22 '16 at 13:56
• We really confirmed it for Curiosity, in a scary way, when we used the wrong number and saw the effect! – Mark Adler Apr 22 '16 at 14:20
• You'd even need to know the mass/gravity of Mars to enter orbit successfully. Or even do a close-ish fly-by without hitting the planet. I don't get this question, its tone sounds like it's skeptical of "physics" and it's "theoretical calculations" having some agenda. – Nick T Apr 22 '16 at 18:58
• Also, with orbiting bodies (like Phobos and Deimos) determining gravity remotely is quite easy. It's much trickier for moonless planets. – SF. Apr 23 '16 at 18:38
• It looks like MSL's IMU was used to conduct surface gravimetry experiments - paper forthcoming. – pericynthion Dec 12 '16 at 18:28

## 3 Answers

The "gravity of Mars" is not a number but rather a complex field. The most recent is remarkably detailed, made up to spherical harmonics degree and order 120, described by 29,512 coefficients:

These maps are made using orbiters (three orbiters in this case), not landers. A lander/rover can give just one local gravitational acceleration and direction, which will never be a textbook value.

The orbiter data also show how the gravity field varies with time as mass moves between the atmosphere and the ice deposits at the poles.

So, no, the Mars rovers can do little to "confirm" the gravity of Mars. Unless you just want to check that it's somewhere around $3.7\,\mathrm{m/s^2}$. Our Mars orbiters have "confirmed" the gravity of Mars, or really measured it, to very high accuracy, far above our rovers' poor power to add or detract.

• The earths surface also is a complex field, and similar maps are available of the earths surface showing higher and lower gravity, however, this does not answer the original question. The gravity on mars is theoretically calculated to be 0.3895 of the earths gravity. The earths gravity is expressed in SI units as 9.80665 m/s2. Mars is theoretically calculated at 3.728 m/s2. I'm asking if this theoretical value was confirmed by the rover. I've seen several articles with the same image you provided but of all the videos and articles I've read, they don't state the strength of Mars' gravity in SI – Chris Apr 22 '16 at 13:36
• That gravity value is for an imaginary location at some mean altitude with all local perturbations due to terrain or mass concentrations zeroed out. There is no lander at that imaginary location. The point is that the gravitational acceleration is different at each landing site, and none of them are that number. – Mark Adler Apr 22 '16 at 13:43
• @Chris The complex measurements provided are clearly enough to confirm the mean theoretical value. If you have doubts that these measurements were actually used to confirm it, you should clarify. – called2voyage Apr 22 '16 at 13:59
• Such a pretty answer (+1)! However, the image shown does not portray surface gravity. To do that, one needs to incorporate centrifugal acceleration that results from Mars' rotation. To do an even better job, one needs to incorporate variations due to terrain. That's a tough job, but people from the Western Australian Geodesy Group have done just that: geodesy.curtin.edu.au/research/models/mgm2011 . – David Hammen Apr 22 '16 at 18:06
• Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Apr 22 '16 at 19:26

Did the rover actually do a test to confirm the theoretical gravity is truly equal to the actual measured gravity?

First off, what would be the point?

Secondly, of course they did, but not to perform that test. The Mars rovers were/are autonomous. They needed to know where they were without outside help. To accomplish this, Mars rovers are equipped with inertial measurement units (IMUs). One of the key components of an IMU is an accelerometer.

At periods when a rover was stationary, the accelerometer "measured"1 gravity. This question asks for the boring part of that reading, the magnitude of that vector. The important part of those stationary readings was the direction of the measured acceleration. Ignoring the deflection of the vertical, those steady-state measurements gave an indication of the rover's orientation2.

The accelerometers were also used while the rovers were in motion. Integrating sensed acceleration, less gravity, is a crucial part of inertial navigation. For example, see Attitude and Position Estimation on the Mars Exploration Rovers.

1 I used "measured" in quotes because you cannot "measure" gravity directly. This is one of the consequences of Einstein's equivalence principle.

2 Deflection of the vertical on Mars can be huge by Earthly standards (0.3 degrees near the peak of Olympus Mons). However, even that extreme value is rather small, and the value on terrain navigable by a rover is tiny. It was safe to ignore deflection of the vertical.

• For most purposes (is there a slope I might slip down? Will I tipple over if I carry some weight on a robot arm? Where will that thing land if I drop it?) the deflection is of no interest and the measured direction is the "correct" direction of gravity to use, that is the deflection is not only safe to ignore but in fact would be wrong not to ignore. – Hagen von Eitzen Apr 24 '16 at 19:18
• Of course it's of interest. If you want to point your high-gain antenna at Earth, you had better know the local deflection of the vertical. – Mark Adler Apr 25 '16 at 6:27
• @MarkAdler - You're thinking of slope, which can be up to 20 or 30 degrees for the terrain navigable by Curiosity. Deflection of the vertical is the tiny difference between astronomical latitude and geodetic latitude. The maximum value in the Gale Crater area is about 250 arc seconds. It's less than 100 arc seconds In the area where Curiosity has been / will be. That's a tiny error compared to the 2 degree HGA pointing requirement. It's probably not even observable given the requirements on the IMU. – David Hammen Apr 25 '16 at 11:18
• No, I was thinking of deflection of the vertical, in order to interpret your accelerometer reading, to make a point. However you're correct that for our little high gain antennas, it makes no difference. – Mark Adler Apr 25 '16 at 13:17

Did the Mars rovers actually confirm the gravity of Mars?

## Yes, it did (finally, yay!)

tl;dr: As far as I can tell, the data here represents ground-truth acceleration measurements from the surface not using the super-colorful (accurate) space-based measurements of gravitational spherical harmonics described in this answer, not even for calibration. Therefore I think this is independent confirmation of the strength Mars' gravity on the surface.

It's important to remember (as pointed out in this comment that centrifugal effects due to the rotation of Mars will also show up in the accelerometer data. The 2019 paper in Science (below) is paywalled and there's no mention of it in the 2016 conference paper (below), but with $$GM$$ = 4.282837E+13 m^3/s^2 and $$R_0$$ = 3396200 meters, and the altitude of Curiosity's location near the bottom of Gale Crater of about -4500 meters, acceleration due to gravity alone should be about 3.723 m/s^2. Centifugal effects should be of the order of -0.014 m/s^2, so the accelerometers should read about 3.709 m/s^2. The problem is that the numbers below are half-way in-between 3.723 and 3.709, so this will have to wait to be resolved.

As pointed out in @DavidHammen's answer and comments there, curiosity does have at least one operational 3-axis set of accelerometers. the primary purpose is to measure the direction of the local gravitational vertical with respect to the rover's frame.

This is used in navigation, especially when roving on a significant incline to keep from rolling over, and probably in the math to connect images from the various cameras to the local terrain.

It's also used to properly point Curiosity's high gain antenna directly at Earth when it occasionally phones home without linking/relaying through satellites in Mars orbit.

Scientists working with the Curiosity rover used a piece of its navigation equipment—an accelerometer like the one in your cellphone—in order to make an important measurement about Mars’ mysterious geology.

Curiosity is currently roving around Mount Sharp, a 5-kilometer-high (3-mile) mountain in the center of Gale crater. But it’s unclear whether the mountain is the result of the crater once being filled in and losing matter to erosion, or whether the mountain is more like a large dune of deposited material. Curiosity doesn’t possess a scientific instrument to determine the nature of the mountain—but it does have force-measuring navigation equipment. So the scientists got creative.

“I realized you can download an app on your phone and, not with much precision, but you can measure [the force of Earth’s gravity] because your phone has accelerometers,” the study’s lead author Kevin Lewis, assistant professor at Johns Hopkins University, told Gizmodo. He figured he could do the same thing with Curiosity’s accelerometers, and perform some interesting science.

Gravimetry, or precisely measuring changes in the local gravitational field, is a useful way to understand the rocks beneath the surface, since an object’s force of gravity increases with its mass. Apollo 17 had a gravimetry experiment to study the Moon, for example—but Curiosity does not have a gravimeter. It does have a navigational system, however, which includes gyroscopes and an accelerometer for measuring changes in velocity, acceleration, and orientation.

The navigational system isn’t quite as sensitive as a gravimeter would be, but the scientists made do. They acquired the data on the accelerations experienced by the rover, then adjusted it to account for things like Curiosity’s location on Mars as well as potential effects of temperature and elevation on the equipment.

The accelerometers may not have been originally designed for this kind of measurement. They are likely to have been well calibrated because NASA doesn't fool around (except maybe here with the purple lasers with lousy/random beam-profiles).

It's a challenge to calibrate accelerometers perfectly at sub 1-g values. You can rotate them to use $$\cos(\theta)$$ but imperfect devices can't always reject sideways acceleration perfectly. See the (currently unanswered) question How was InSight's vertical seismometer (accelerometer) tested in Earth's stronger gravity? by K. W. Lewis, S. F. Peters, K. A. Gonter and the MSL science team.

You can read about the first results in the 47th Lunar and Planetary Science Conference (2016) conference paper First Gravity Traverse on the Martian Surface from the Curiosity Rover.

There is a (possibly) more detailed paper published today in Science A surface gravity traverse on Mars indicates low bedrock density at Gale crater with some important results, but unfortunately though the mission and researcher is mostly taxpayer-funded, we have to pay again to read about it. (i.e. paywalled).

From the 2016 conference paper:

RIMU accelerometer data is intended primarily for use in determining rover roll and pitch from the relative magnitudes of the three axes under the static acceleration g of the Martian gravitational field. However, the relative magnitude of g will change with both position (resulting from subsurface density variations) and elevation, which could be detectable with sufficient precision. Although the raw accelerometer data from the rover is insufficiently sensitive, we have developed a series of calibration procedures to account primarily for 1) temperature sensitivity effects and 2) slight biases among the three accelerometers when the rover is non-horizontal. Similar correction procedures have been successfully demonstrated for navigation-grade IMU data in terrestrial airborne gravimetry experiments(4).

Figure 1 shows the variance reduction associated with the three largest corrections to the RIMU data set. An additional correction is applied to remove a sinusoidal seasonal trend likely resulting from longer-term temperature hysteresis. After applying these corrections, we are able to achieve a relative precision of roughly 10 mGal (10-4 m/s2). Although coarse by modern terrestrial gravimetric standards, this is roughly equivalent sensitivity to that reported for the Apollo 17 traverse gravimeter.

Figure 2 – Determination of the relationship between gravitational acceleration and elevation. a) Rover elevation data as a function of Sol. b) Calibrated gravity measurements as a function of solar longitude (Ls). Elevation data is fit over one Martian year to avoid seasonal trends. The falloff in g as Curiosity has climbed Mount Sharp can be explained most simply by a low subsurface density for Mount Sharp (best fit – 1600 kg/m^2).

below: "Measurements of Mount Sharp’s gravity using Curiosity data. Graphic: Kevin Lewis" from Gizmodo