# Gravity Model measurement technique

Geopotential model are used whenever propgation has to be done of the orbit. Geopotential model models the potential of earth via spherical harmonics.

These models are generally published by NASA as measured by mapping missions.

One can easily find geopotential model for earth, moon, mars and venus.

How does one map these geopotential model ?

What technique is used to map gravity ?

Well obviously an orbiting satellites measure zero acceleration when not firing engines as orbit is nothing but free fall.

So how can one map gravity ?

Edit:

Following is quoted from wiki article about grail mission technique. The answer probably only addressed about earth gravity modelling. I was more interested in gravity mapping of moon and other bodies.

Each spacecraft transmitted and received telemetry from the other spacecraft and Earth-based facilities. By measuring the change in distance between the two spacecraft, the gravity field and geological structure of the Moon was obtained. The two spacecraft were able to detect very small changes in the distance between one another. Changes in distance as small as one micron were detectable and measurable. The gravitational field of the Moon was mapped in unprecedented detail

How can simple change in distance can give the gravity map?

• I have edited the question. And question is not broad i asked for the technique that NASA uses to map gravity Apr 29, 2018 at 16:36

Since the gravity field is the vector gradient of the gravitational potential field, precise measurements of a spacecraft's trajectory in 3 dimensions and time provide a good sample of that gravity field along the spacecraft's path. Tracking for a long period of time, over a path that covers longitudes and latitudes (so a polar orbit is best for this) gives such samples that blanket the planet. At JPL the orbital dynamicists have a big software package called "ODP" ("Orbit Determination Program" - how's that for a pedestrian program name?) that will take all the position and velocity data points, determine the gravity field magnitude and direction at each point, and then fit a model of the potential field to those gravity field data. They can take two approaches: one is to fit the observed gravity field with a spherical harmonic model of the potential field, to really high order, and the other is to model the mass distribution in the planet, dividing the planet into cells of appropriate size (corresponding to the spatial resolution of the data) and increasing or decreasing the mass within each cell until it produces a geopotential field and gravity field model that matches the observations. Bob Jacobsen has extensive experience using ODP. See for example Cassini Orbit Determination Performance (July 2008 - December 2011) and also Orbit Determination and Parameter Estimation for further reading.

How do you get the trajectory data? Mostly via radiometric tracking. A ground station can send to the spacecraft a signal modulated with a "ranging code" on top of the carrier frequency, and the spacecraft sends it back to the ground via a transponder. The two-way propagation time of the signal gives a very accurate measurement of the distance from the ground station to the spacecraft, and the observed Doppler shift of the carrier gives a very accurate measurement of the component of the spacecraft's velocity radial to the ground station.

• This is a great answer! I hope you don't mind, I added a few supporting links.
– uhoh
Apr 30, 2018 at 0:51
• What about moon venus and mar Ranging is not very accurate for so far bodies ! Apr 30, 2018 at 1:12
• Oh good. Tom is here. I can go now. Apr 30, 2018 at 5:02
• Nope! Nope! Nope! @Mark Adler! It takes a village, and you and I are two of the villagers. To uhoh (this site won't let me refer to more than one user in an edit), one of the parameter sets ODP models is the position and velocity of the barycenter of the body the spacecraft is orbiting, so it can actually improve the ephemerides. Apr 30, 2018 at 5:20
• GRAIL had two elements (spacecraft) because the physics of orbital dynamics over a non-uniform body causes the distance between two such co-orbital objects to vary with the mass concentration beneath them, much more than their altitude varies. The two GRAIL elements communicated with each other to measure that inter-spacecraft distance (relative positions) very, very accurately, and with the DSN to get absolute positions to less accuracy. You're right, this is a different technique from the one used for Cassini et al. Apr 30, 2018 at 6:17

Well obviously an orbiting satellites measure zero acceleration when not firing engines as orbit is nothing but free fall.

That's not completely true. A accelerometer located away from the spacecraft's center of mass experiences accelerations due in part to the fact that the gravitational acceleration at the accelerometer location is slightly different from the gravitational acceleration experienced by the spacecraft itself. A sufficiently sensitive accelerometer can measure this gravity gradient. ESA's Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission used extremely sensitive accelerometers to measure variations in the Earth's gravity gradient.

How can simple change in distance can give the gravity map?

This part of the question refers to the GRACE and GRAIL pairs of satellites used to generate models of the Earth's and the Moon's gravitational fields. As an aside, those satellite pairs measured range rate as well as the distance between the satellites. When a satellite passes over a mountain, or some other concentration of mass, that mountain will make the satellite speed up a bit as it approaches the mountain and slow down a bit after it passes over. A pair of satellites orbiting one after the other will experience the effects of the mountain at slightly different times. The distance between them will get elongated and then relax back toward nominal.

Suppose you have a model of an object's gravitational field and gravity-sensitive measurements (e.g., gravity gradiometer measurements such as GOCE, range/range-rate measurements such as GRACE and GRAIL, pings from Earth, ...) of spacecraft orbiting that object. The orbit calculated from the model will inevitably disagree with those observations.

The errors between the calculated state and the observed state yield clues regarding how to adjust the model coefficients so as to reduce those errors. A number of techniques such as Kalman filters and batch least squares estimation have been developed that do just that. Now do the same with the refined model, and refine again. Eventually no further improvement can be made to the model.

• When accelerometer is located away from centre of mass. And the body is not rotating it will still measured acceleration will be zero. It is the centrifugal force. Apr 30, 2018 at 17:38
• @Prakhar -- That is not the case. The gravitational acceleration of the satellite's center of mass is very close to that of a point mass located at the satellite's center of mass. Being a rigid body, the entire satellite undergoes this acceleration. An accelerometer located away from the center of mass will undergo a slightly different gravitational acceleration because the vector from the center of the Earth to the vehicle's center of mass is different than is the vector from the center of the Earth to the accelerometer. Apr 30, 2018 at 19:11
• Oh I understand. So, the accelerometer will feel a push as if the gravity is trying to take away the spacecraft from him ! @davidhammen May 1, 2018 at 2:42