Interpreting Gravitation: Orbits & Ellipticals

[sciencecrazy]

*Has General Relativity got some interpretations saying planets and satellites don't act as single mass?

*Also can it be that orbits of all orbiting bodies are elliptical or seem elliptical due to moving central body?

 

[mathman]

When dealing with something like the solar system, i.e. massive central body (sun) with small orbiting bodies (planets), the first order solution is to treat each planet separately as orbiting the sun (assumed fixed). The stable orbits will all be ellipses. More precise orbits are calculated by taking into account the effects of the planets on each other. The motion of the whole system relative to outside influences, like within a galaxy, does not affect the internal structure in any significant way. To answer your specific question, the ellipses are relative to the sun.

 

[higginsdj]

But of course relativity still has to be taken into account to calculate precise orbits.

Cheers

David

 

[D H]

But of course relativity still has to be taken into account to calculate precise orbits.

Yes and no. The effects of general relativity on solar system bodies are rather small. The effect is greatest on Mercury, and at that it is a precession of only 43 arcseconds per century. It is more important is to have very good estimates of the gravitational masses of the bodies that comprise the solar system (expressed as the product G*M) and to have an extremely good propagator on hand. Fairly precise orbits can be obtained by using a good propagator against Newtonian gravity backed up with good estimates of the solar system masses. On the other hand, general relativity won't help overcome poor estimates of the masses or a lousy propagator.

That said, if you want precise orbits that span a long period time you do need all three (plus some very good estimates of the orbit themselves). If you want precise orbits for a very, very long time, even having all three won't help. The solar system appears to be a chaotic system.

 

[higginsdj]

Yes and no. The effects of general relativity on solar system bodies are rather small.

There is no "no" about it. NEO's and Comet orbits have this applied. Why? because when we calculate the probability of collisions with Earth we want to know exactly where these objects are going to be.

Cheers

David

 

[Nabeshin]

There is no "no" about it. NEO's and Comet orbits have this applied. Why? because when we calculate the probability of collisions with Earth we want to know exactly where these objects are going to be.

Cheers

David

I'm very skeptical of this. I find it very difficult to believe that the relativistic corrections would be on the same order as, if not larger than our known error in the positions and velocities of these objects...

Could you site a source stating that relativistic corrections are applied to these NEO calculations?

 

[higginsdj]

My only reference is correspondance I have seen from those making the calculations (MPML group). I am certainly not arguing the scale of effect.

(Note that they - MPC, NEODys etc - do plot the orbits of these objects out to 100 years in the future - sometimes more to make collision predictions)

Cheers

David

 

[D H]

There is no "no" about it. NEO's and Comet orbits have this applied. Why? because when we calculate the probability of collisions with Earth we want to know exactly where these objects are going to be.

JPL uses the Standard Dynamical Model to model the orbits of NEOs and comets because they use the Standard Dynamical Model for the Development Ephemerides. Failing to incorporate general relativistic effects in the orbits of these small bodies would result in inconsistent physics. The physics used in the models has to be consistent since it is the relative state one is after to determine whether a collision is imminent (say in the next 25 years). I calculate about an error of about 1000 km would arise after 25 years if relativistic effects are used to model Earth's orbit but not that of the NEO.

Suppose instead that the ephemerides had been built without modeling relativistic effects. Now we need to ignore relativistic effects on the NEO to have consistent physics. Because there some unmodeled physics is occurring, the errors in the planetary positions will grow with time, but over the 25 year interval of concern that error will be fairly small. More importantly, because a NEO will be subject to just about the same relativistic effects as is the Earth, the error in the relative state will be small -- so long as we ignore relativistic effects for both the NEO and the Earth.

There are non-gravitational forces that affect these small bodies that are not modeled in the SDM. NEOs are subject to solar radiation pressure and the Yarkovsky effect. These become very significant for small NEOs, swamping relativistic effects. For example, the uncertainty in solar radiation pressure and the Yarkovsky effect for 99942 Apophis are of the same order as are the known relativistic effects.

The biggest unknown for most NEOs isn't the unmodeled physics. It's that the state isn't well known. Consider 99942 Apophis again. Because for a while it looked like it might indeed be on a collision course with the Earth, Apophis has been the subject of about 1000 telescope sightings and 7 radar fixes. Even with all of those observations we don't know Apophis' orbit all that well. It doesn't really matter whether relativistic effects are modeled or not as far as NEOs are concerned, at least for the short term (< 100 years). After 100 years it doesn't matter whether relativistic effects are modeled or not either because after that the errors swamp everything.

 

[higginsdj]

I'm not in a position to argue whether it should or shouldn't be used or how much impact the addition will have, I simply stated that it was used. The published ephemeris are simply used to calculate current positions and are not used for long term predictions.

Some people (and not sure if that includes the MPC and NEODys) are using radiation pressure modelling in their predictions for Potentially Hazardous targets. It is not a matter of determining the exact position of the object at a point in time but rather feeds into the errors of the orbital predicitons to know whether a collision is possible.

Also, 99942's orbit is a U=1 and its current positional uncertainty is ~52.0". Its not a U=0 but I would say "we don't know Apophis' orbit all that well."

 

[D H]

Once again, the primary reason general relativistic effects are used for NEOs and comets is because the researchers who follow these objects already have on hand a suite of tools that incorporate general relativity in the form of a post-Newtonian expansion in the equations of motion. Omitting relativistic effects on those NEOs and comets would require a good amount of effort and would result in inconsistent physics.

Regarding propagations longer than 100 years: Yes, some people do just that (e.g., 2002 AA₂₉, which has been predicted by some to become a quasi-satellite of the Earth 600 years from now). The validity of those claims is IMO more than suspect. There's just too much uncertainty in state and in the dynamics so as to make those claims utterly worthless.