# Gravity assist (flyby/slingshot) from an asteroid?

Could a spacecraft perform a gravity assist maneuver in an asteroid? Has it ever been done? I tend to think that the asteroid would need to be quite massive for a "significant" change of delta-v.

• I'd expect that in any of the asteroid fly-bys collecting images and data, the asteroid had a gravitational effect on the passing spacecraft, but I also suspect that it was very small and needed to be considered for the change on the flight path and not so much as an assist. As you suggest, small mass means very small change. Commented Dec 23, 2022 at 18:33
• Here is another impractical idea - Asteroid as a "free slingshot?" Commented Dec 24, 2022 at 3:14

Asteroids are too small to give a meaningful boost from a flyby.

During an encounter, the relative entry and exit speed is equal

$$v_{in} = v_{out}$$

The only thing a mass does it bend the direction of this vector a little, possibly resulting in a little speed boost when translated back to the outside frame of reference (Sun relative).

This turning angle can be calculated like this:

$$\theta =2 \sin^{-1}\left(\frac{1}{1+r_{P} \cdot v_{in}^2/\mu}\right)$$

So let's work out an example for one of the big boy asteroids, 3 Juno

• $$\mu = 1.9 \cdot 10^9 m^3/s^2$$
• $$v_{in} = 2000 m/s$$
• $$r_P = 150 km$$

A measly 0.36º of turning, that's some ~12 m/s of speed boost with an optimal flyby.