# What is the smallest object a spacecraft can orbit?

According to this article, NASA’s *Dawn * spacecraft will orbit the Vesta asteroid sometime in 2011. Vesta, while large for an asteroid, has a mean diameter of only 330 miles, and a mass that is only 0.008% that of Earth.

Obviously, that is large enough to maintain a spacecraft in orbit. But what is the minimum size of a space object that a typical unmanned spacecraft can orbit? Is that about the limit, or could we orbit a comet that was only a few hundred meters in diameter?

Depends on how you define “orbit”. If the spacecraft had less mass than the object, then the object would be orbiting the spacecraft instead of the other way 'round.

If two objects have equal mass, they can “orbit” a point in space that is halfway between them. Even the earth causes the sun to wobble a bit, and both the sun and the earth are orbiting a point that is defined but the center of mass of the two-body system (ignoring the other planets). For example.

But objects on the scale of spacecraft cannot orbit each other, can they? At some point, the gravitational pull of very small masses is simply not great enough to make any discernible difference in the trajectory of either spacecraft.

If they are close enough, or moving slowly enough it doesn’t matter.

The gravitational attraction is GMm/r^2. If M and m are reduced by 100 and r is reduced by 100, everything is exactly the same.

It depends upon your scale. Ywo very small objects far away from anything else can orbit around their center of mass. They’ll just have a very, very large orbit, the size fixed by their velocities and the depth of their dimple of a gravity well. The only time this would not, for practical purposes, work was if other ambient effects (Light pressure, say) were comparable in size.
If you placed two spacecraft halfway between the sun and Alpha Centauri, I’ll bet you could get them into a stable orbit.

G = universal gravitational constant
M = mass of larger object
m = mass of smaller object
r = distance between the objects.

(Just in case you’re not familiar with this equation)

As long as they were moving very slowly-- ie, slower than the escape velocity for the system.

And therin lies the rub, I guess; the escape velocity for small objects is so slow, it is probably not feasible to build rocket motors small enough to maneuver without blasting out of “orbit”.

The sun has only about 1,000 times more mass than Jupiter, so you can imagine a spacecraft orbiting an object that is only 1,000x as massive in the same way Jupiter orbits the sun.

Or, think of binary stars that are roughly of equal mass. Then just scale it down.

You can calculate the escape velocity:

ve = sqrt(2GM/r), where M = mass of the object you are escaping from

That’s especially true for the “larger is better” efforts of the Soviet Union.

Asteroid 1313 Berna has a diameter of 11km, as does its moon. They orbit each other at a distance of ~35km.
Many asteroids have moons.

I think the OP might be getting too caught up in the whole orbit thing, too. If the object were small enough, and as long as it wasn’t moving real fast (relative to the earth), we could just approach it and cozy up along side it like we do with the space station. There isn’t a need to orbit something in order to investigate it.

But, if you really, really wanted to make sure we could orbit something, let’s work backwards. Let’s assume that we need to orbit it at least from 1 km away. And let’s assume that we have an engine that can create a velocity of .1 mi/hr accurately. (I just guessed at that). That’s about .5 m/s.

Using the formula for escape velocity (assuming ve = .5 m/s), we get a mass on the order 1.8x10^12 kg as the smallest practical mass we could orbit. As a reference, the earth is about 6x10^24 kg.

Oops. .1 mi/hr is about .05 m/s, so it should have been 1.8x10^10 kg.

It was a thought experiment more than a practical application. I was curious about the nature of orbiting small objects, not why we might wish to do such a thing.

OK. I think the calculations I did should ballpark what you were asking about. Note that it would be much, much smaller than Vesta.

the geodesics become rather fuddled when computing orbits for low mass objects… Obviously the relative masses don’t matter as much as perturbations from other sources. Sure something with .ooo8 earth masses stll masses large enough to form a long, slow, large orbit around, but gravitational attractions from other bodies, even very distant, if they are massive enough will make that orbit unstable over time… a few days easy, a few weeks harder, a few months, pretty tough, and anything longer very hard indeed. The correctional thrusts required to maintain a stable orbit will have to be tightly controlled in both vector and force, as even a few thousandths of a percent error will cause as much pertubation as the correction will require.

fml

A spacecraft has already orbited an object much smaller than Vesta. NEAR-Shoemaker orbited the asteroid 433 Eros in 2000. Eros only masses 7.2 * 10[sup]15[/sup] Kg while Vesta masses 2.7 * 10[sup]20[/sup].