# Clohessy - Wiltshire equations for use in Asteroid "chasing"

So I'm actually a student studying this sorta thing, and an assignment I have is to chase/rendezvous with an asteroid. I've done my reading on the C-W equations (what little I could understand) and from what I can gather, these are general equations who care not for what they are being used to chase.

Essentially my question is, am I correct in thinking that they can be used to calculate motion/delta V to close the distance on an asteroid, just as well as the ISS/any other Space Station?

Yes, I believe. Mathematically, orbits around single bodies "care not".

Your link says that this is only a first order solution (an approximation) and applies only to approaches to objects in circular orbits (by objects which are in elliptical or circular orbits) and so you have to keep that in mind, but since the Sun's gravity field is much closer to being spherically symmetric at asteroid distances than Earth's gravity field is at LEO distances, it is even more appropriate to use the way you are proposing than in Earth orbit in some ways.

However, your particular asteroid will need to be in a circular orbit for this approximation to work correctly.

Go for it! If you have any problems, post a new question showing some details of your calculations.

• Ah, one final question, prior to me attempting my calculations. The asteroid is spinning, does that affect the moving frame of reference? Feb 9, 2018 at 13:13
• @HarveyRael. Asteroid rotation does not affect the dynamics as stated by HCW equations since you do not care about asteroid gravity field. However, if you want to chase a point relative to the asteroid, you have to keep in mind that this point will be rotating in the HCW frame. The equivalent of the HCW equations for elliptic orbits are the Tschauner-Hempel equations, although they are a LTV system, a "simple" state transition matrix was derived by Yamanaka-Ankersen in 2002: "New State Transition Matrix for Relative Motion on an Arbitrary Elliptical Orbit". Feb 9, 2018 at 14:21
• @uhoh Your help was excellent. Did some calculations, and they turned out to be fairly reasonable, while not seeming too large or too small. I am considering writing a full blown paper on it now! Feb 11, 2018 at 12:03
• @uhoh I went from hot, to not so hot in a day! For some reason, my delta v figure is only time variant, and appears to be distance invariant. That shouldn't be the case I'm pretty sure? Can I post an example of my calulations? Feb 12, 2018 at 15:29
• @uhoh update for you as I thought you might be interested, given how much you helped! The problem this question solved was part of a group project which has since been accepted to be published in the conference proceedings at the 69th IAF Conference this year! So many many thanks! Jul 24, 2018 at 0:41