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Vessels and asteroids have mass but no gravity.

So answer is: No.

Only workaround: Make your orbit so that your AP is 20m higher and PE 20m lower than the station orbit. But you have to be very precise.

You will "orbit" your station once per orbit then.

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Even in the real world, you would need a very large space station to be able to semi-stably orbit it. For example, the Hill sphere of the ISS is 1.86 meters, so to orbit around the ISS's center of mass in a stable fashion, you have to be literally inside the ISS.

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10 hours ago, Starman4308 said:

Even in the real world, you would need a very large space station to be able to semi-stably orbit it. For example, the Hill sphere of the ISS is 1.86 meters, so to orbit around the ISS's center of mass in a stable fashion, you have to be literally inside the ISS.

In the real world, you could get there indirectly by putting a station exactly at one of the Lagrange points.  Objects can orbit the Lagrange point, so they act like they're orbiting the station, even though the station's gravity has virtually no effect.  

But you can't do this in KSP either (without a mod like Principia), because the game only models the gravity of the body whose SOI you're in, meaning there are no Lagrange points. 

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13 hours ago, Draalo said:

Vessels and asteroids have mass but no gravity.

So answer is: No.

Only workaround: Make your orbit so that your AP is 20m higher and PE 20m lower than the station orbit. But you have to be very precise.

You will "orbit" your station once per orbit then.

I knew this, but never really considered doing it...  I kinda want to try now.  Thanks!

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23 hours ago, boccelounge said:

I knew this, but never really considered doing it...  I kinda want to try now.  Thanks!

For a visible demonstration of what this looks like, without needing to set up precise orbits of things, try running the New Horizons mod.  It's a mod that completely rejiggers the solar system, with Kerbin becoming a moon of a ringed gas giant.  That gas giant has several moons besides Kerbin.  One of them, Aptur, is a little Gilly-like thing that has an orbit whose period precisely matches Kerbin's, but which is more eccentric and slightly inclined, with the result that from Kerbin's point of view it appears to "orbit" Kerbin once for each revolution around the gas giant.

Makes for an interesting navigational challenge.  :)

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