General Question Orbital stability

[sorindafabico]

I noticed some difference between LEO and low Moon orbits: orbits around the Moon are much more stable than LEO orbits (I always play with all perturbations on). It's much easier to do sync and rendezvous planning around the Moon than in LEO. Periapsis precession seems to be slower in LLO, per example.

Is it something linked with the small rotational speed of the Moon? Shouldn't Earth's gravity be a stronger source of perturbations there than the Moon in LEO? Also, a read somewhere that orbits around the Moon aren't stable in the long term, but I'm not sure about this...

 

[Kyle]

Earth has an atmosphere.

 

[Cras]

Non-spherical gravity. As far as I know, it only applies to Earth inside orbiter, so if you have that turned on you will find orbits around Earth to be a bit less stable. Also as Kyle pointed out, the atmosphere. In orbiter it goes up to 2000 km, so even in LEO you will get drag.

 

[Shifty]

Also, a read somewhere that orbits around the Moon aren't stable in the long term, but I'm not sure about this...

The real Moon has concentrations of mass near its surface caused by ancient huge asteroid impacts. This causes its gravitational field to be relatively non-uniform. The non-uniformity of the gravitational field contributed, for instance, to the Apollo 11 landing being miles from its intended landing site. It also causes orbits around the moon to be unstable.

In Orbiter, however, the moon's gravitational field is uniform and spherical. I wonder how difficult it would be to model the mascons...

 

[sorindafabico]

I suspected that the atmosphere was part of the cause. But, if non spherical gravity applies only to Earth, we got the answer IMO.

 

[orb]

But, if non spherical gravity applies only to Earth, we got the answer IMO.

It doesn't apply only to Earth. It applies to all bodies using JCoeff parameters in their configuration files defining Legendre polynomial series expansion coefficients (however all other Orbiter planets than Earth define only the J₂ coefficient) for the perturbations.

See "Doc/technotes/gravity.pdf" for details about the non-spherical gravitational perturbations.

 

[Cras]

Well, the moon does not have such paramter in its config file, so that is why Moon orbits are more stable than earth.

Non-spherical gravity will do some weird things in Orbiter as well over long periods of time.

 

[orb]

Well, the moon does not have such paramter in its config file

But of course you can add them where they are missing or update with values from the table below.

Body|J ₂ |J ₃ |J ₄ |J ₆

Mercury|60e-6| | |

Venus|4.46e-6|-1.93e-6|-2.38e-6|

Earth|1082.627e-6|-2.532e-6|-1.62e-6|-0.21e-6

Moon|203.43e-6| | |

Mars|1960.5e-6|31.5e-6|-15.5e-6|

Jupiter|14696.4e-6| |-587e-6|34e-6

Io|1860e-6| | |

Europa|436e-6| | |

Ganymede|128e-6| | |

Callisto|33e-6| | |

Saturn|16290.7e-6| |-936e-6|86e-6

Uranus|3343.5e-6| |-28.9e-6|

Neptune|3410e-6| |-35e-6|

Source

 

[sorindafabico]

Just put the values like this?

JCoeff = 1082.627e-6 -2.532e-6 -1.62e-6 -0.21e-6

 

[JonnyBGoode]

So adding the line "JCoeff = 203.43e-6" in the Moon.cfg file would solve this?

 

[Cras]

But of course you can add them where they are missing or update with values from the table below.

Sweet, I will. :thumbup:

 

[Shifty]

Page 120 of this pdf has a few more J2 values for other solar system bodies:
http://www.gps.caltech.edu/classes/ge131/notes/Ch11.pdf

The problem is that the Legendre coefficients only correct for spherical harmonics of the ideal spheroid gravity source. And they assume spherical symmetry. Neither are true of Lunar mascons (and less significant irregular features of Earth's gravity field.) On the other hand, verisimilitude to the nth degree is certainly not necessary to my enjoyment of the simulation.

 

[sorindafabico]

Testing non-spherical gravity. The red line is a function of a vessel's altitude in time with the default Moon.cfg. The green line is the same function with the parameter "JCoeff = 203.43e-6" added in Moon.cfg. It's a polar orbit. The vessel is above the equator in t=0 and, initially, the orbit had ecc=0.

Both were produced from the same scenario:

BEGIN_ENVIRONMENT
  System Sol
  Date MJD 52006.7487240331
END_ENVIRONMENT

...

PB-01:ShuttlePB
  STATUS Orbiting Moon
  RPOS -1770617.01 -48517.42 -325117.00
  RVEL -43.722 1649.391 -8.028
  AROT -143.94 -12.06 136.87
  AFCMODE 7
  PRPLEVEL 0:1.000000
  NAVFREQ 484 124
END

I noticed the range from PeA to ApA was increasing each orbit in both lines, and both orbits cross at each completed period. I suppose the perturbations on the red line must be caused by the Earth and the Sun.

 

[sorindafabico]

After the last post, I became curious to see the behaviour of orbital energy in LEO and got unexpected (for me) results.

I don't know if I made some mistake, so I will describe the process:

I got velocity and altitude data with FlightData from ISS in some stock scenario (Brighton Beach, if I remember well). Then, I would calculate the specific orbital energy (the energy for each mass unit) for each data point and make a graph.

As I would need the semi-major axis to calculate

, I got the semi-major axis for each data point using

(from the vis-viva equation). Both were acquired by making a loop and using an array.

Then the results were:

Semi-major axis:

Orbital energy:

I was expecting a continuous loss of orbital energy (due to drag) and got a sine wave. Is this right? Do I need to get a bigger amount of data or I did something wrong?

 

[ADSWNJ]

By the way - the real trajectory guys on LADEE said on their blog (Astrogator's Guild) that they model the moon as a sphere with uniform gravity until it becomes the dominant effect, then switch to much more detailed lunar gravitational modeling.