 # Cis-Lunar Propagation Context Clarification

I have implemented the CR3BP propagator and I am requesting some clarification about the context of the Earth-Moon system as described by Orekit. Any help is appreciated.

1. What are the time units when using CR3BP along with an AbsoluteDate? In the HaloOrbit test class, after a multiple shooting the value of the orbital period is 2.7435. Is this in terms of the period of the moon orbiting the Earth? Days? If in terms of Moon-Earth period would this be considered a sidereal or a lunar month?

2. What are the main points that define the coordinate system? Do the position and velocities originate from the Earth/Moon barycenter or from the center of the Earth or Moon? What would constitute a position vector of (1, 1, 0)?

3. How are velocities defined in the E/M rotating frame?

4. Is there currently a way to implement advanced force models in a CR3BP integration in Orekit?

5. I assume the mu value in CR3BP is the mass of Earth over the total system mass, i.e. Me / (Me + Mm), which is equal to 0.01215. Am I correct?

Regards,
Connor

Hi Connor,

I hope this will help you and that it is not too late !

1. The CR3BP requires normalization before computation, that means every output you get depends on the CR3BP system you are using. For example, in the Earth-Moon system, standard time is the orbital period of the Moon around the Earth, standard distance is the distance between Earth and Moon (which is considered fixed as we are in circular hypothesis). The functions listed in the “Method Summary” part in the link below might help you to get back to common units.

https://www.orekit.org/site-orekit-10.3/apidocs/org/orekit/bodies/CR3BPSystem.html

In other words, your HaloOrbit has an orbital period of 2.7435 lunar months.

1. (0,0,0) is the Earth-Moon barycenter. Distance value 1 is the distance between Earth and Moon. (1,1,0) would then be behind and above the Moon.

2. I’m not sure how to answer to that question. The frame is called Rotating because we want keep the Moon and the Earth fixed in it. It means the rotation of the Moon (and the Earth) around the Barycenter is considered when you make the switch from one frame to another. Also, bodies motions are taken into account in the equations of the force model.

3. I’m not sure to understand what you mean by advanced force model but CR3BP is using different hypothesis and normalizations that makes it very inflexible to the use of other models in it. You can still try if you want to but I wouldn’t trust the results.

4. You are almost correct as you have the right value but the wrong equation, in CR3BP mu = Secondary Mass / ( Primary Mass + Secondary Mass) so 0.01215 in the Earth-Moon system. You can get this value with the command getMassRatio() of the selected system.

Thank you for using Orekit and CR3BP model !

Vincent

Thanks for the clarifications. When you say (1, 1, 0) is above the moon, do you mean that the y-component is orthogonal to the earth-moon plane?