Orbital Mechanics: NASA Launching Probes & GR/SR Considerations

[blumfeld0]

Hi. I was wondering how GR and/or SR is taken into account when the people over at NASA launch probes to comets, or any of the planets?
I know GPS uses GR and SR and I've read a bit about that. But do they need to take into account GR/SR when planning missions or is the Newtonian limit good enough?

thanks

 

[Chris Hillman]

Hope this helps

Hi. I was wondering how GR and/or SR is taken into account when the people over at NASA launch probes to comets, or any of the planets?

You'd have to be more specific. E.g. to describe the orbit of Mercury on a timescale of centuries, you need to take account of gtr. So does that mean that to navigate to Mercury you need to use gtr?

I know GPS uses GR and SR and I've read a bit about that. But do they need to take into account GR/SR when planning missions or is the Newtonian limit good enough?

GPS and other current generation satellite navigation systems are designed for navigation over the surface of the Earth (give or take ten kilometers), so GPS is generally not relevant to space mission navigation.

However, there are some fascinating proposals for deep space satellite navigation systems which would be fully relativistic. See the site in my sig (use the search tool).

 

[pervect]

I don't have much hard information. I don't know for a fact, for instance, whether or not the JPL "Horizons" ephermeris http://ssd.jpl.nasa.gov/?horizons is necessarily used for mission planning.

At this point, I can't even positively confirm that Horizons is based on a PPN model of the solar system, though that's my impression. Use of a PPN model would imply some first order GR type corrections for the sun's gravity.

 

[D H]

JPL itelf uses http://naif.jpl.nasa.gov/naif/about.html" for mission planning. SPICE and Horizons use the same datasets (DE 405, etc) as the basis for the ephemerides. The DE xxx datasets are formed using some kind of weak-field approximation. The datasets themselves are sets of coefficients for Chebychev polynomials that yield approximate planet positions as a function of time. Thus the users of the datasets doesn't need to know anything about gravity. They just need to know how to form the Chebychev polynomials.

 

[Chris Hillman]

Hi, DH, I think that gets back the point I was struggling to express above: for purposes of spacecraft navigation you need an accurate model of the solar system motion on the scale of years. Where that accuracy comes from (recent detailed observations, Newtonian or post-Newtonian theory, or a complicated combination of multiple sources) shouldn't really matter very much. I think that comes down to saying that for injecting a spacecraft into orbit around Mars (once you somehow know where Mars is located at the time when you want to perform the injection), accurately modeling stuff like solar wind buffeting is probably more important than effects arising from the curvature of spacetime.

 

[D H]

Chris, you are quite right. In general¹, spacecraft operators (and the onboard software) don't model relativistic effects period once a vehicle gets close to a planet. Uncertainties in atmospheric drag, thruster performance, sensor performance, gravity², vehicle mass properties, and so on, overwhelm (by many orders of magnitude) the errors induced by ignoring relativistic effects.

Notes:
¹: The GPS satellites are a special case. The clocks on the satellites need to be modeled with extreme accuracy. Were it not for this concern, people wouldn't bother with modeling relativistic effects on the GPS satellites.

²: The non-spherical nature of a planet becomes an issue once one gets close to a planet. Spacecraft designers use a low-order spherical harmonic model of gravity in the spacecraft flight software and a much higher order model on the ground. Gravity is weird enough even without relativitity. For example, see http://science.nasa.gov/headlines/y2006/06nov_loworbit.htm" on the subsatellites released by Apollo 15 and 16.

 

[Chris Hillman]

Hi, DH, thanks for the great link! Do you happen to know to what order JPL (?) carries the spherical harmonics in order to model the gravitational field of the Moon? The Earth? Ditto that the challenges of even Newtonian gravitational physics tends to be underestimated by the public!

 

[D H]

Chris, JPL has developed several models of the Moon's gravitational field based on Lunar Prospector data. The highest degree model is a 165x165 model, LP 165P. Lower degree/order models are a bit more stable. Here's a paper: http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/15597/1/00-1301.pdf . The best models of the Earth's gravity are the EGM96 model (Goddard/Ohio State; multiple satellites; 360x360 model) and GRACE model (JPL/University of Texas, GRACE satellites; 160x160, 200x200 models).

The Earth (and Moon to a lesser extent) are not rigid bodies. The Earth is plastic and is thus deformed by lunar and solar gravity. (Google "Tidal Love numbers" for more info; beware the junk when googling for love.) On the Earth, ice builds up in the winter, melts in the summer. The tidal and seasonal effects show up as time variations in the spherical harmonic coefficients.

 

[Chris Hillman]

Another great link, thanks!

BTW, speaking of deformations due to "body forces", in a thread called "What is the Theory of Elasticity?" in the relativity subforum at PF, I have been slowly working through some background on linear elasticity, hoping to eventually get to nonlinear elasticity and then relativistic elasticity. I might mention a bit about plasticity too. The goal is to provide background for a thread in which pervect, myself, and Greg Egan studied in detail a relativistic rotating hoop, an infamously tricky problem.