# How to calculate the max mass and speed of an asteroid capturable by gravity assist?

After reading this question and the answers, I am wondering about the limits of slingshot method to capture an asteroid into a planet orbit.

Is it possible to calculate if an asteroid can be captured depending on following parameters?

• asteroid mass
• asteroid speed w.r.t. planet
• planet mass
• planet gravity
• minimum flyby altitude

Which would be the apogee and the orbit period depending on these parameters? Are they infinite in case the asteroid cannot be captured? And would a perigee<0 mean "not capturable"?

• As long as the asteroid mass is tiny compared to the planet mass, the number of the asteroid mass is not needed.
– Uwe
May 19, 2022 at 8:53
• how do you know? May 19, 2022 at 9:05

With just the above parameters? No, the asteroid will never be captured.

An asteroid alone slinging by a planet will not be captured, because it needs to reduce its orbital energy relative to the planet and the Keplerian-Newtonian two-body interaction cannot do that without assistance; Orbital energy and orbital angular momentum are constants in Keplerian two-body interactions.

You need some sort of three-body interaction to happen for something slinging by the planet to get captured, such as:

• A moon or other massive object already in orbit of the planet affecting the trajectory of the asteroid. This object can exchange angular momentum and orbital energy with the asteroid relative to the planet, allowing the asteroid to settle into an orbit around the planet, admittedly one that initially crosses the path of the existing moon.

• Another object coming in with the asteroid, such as a massive binary companion, that can carry away the excess angular momentum and orbital energy out of the planet's region, leaving the asteroid in orbit around the planet.

• The asteroid being torn apart by tidal interactions and interacting with its own pieces gravitationally so that some of the asteroid escapes, and some of it gets captured, as above.

• Odd edge effects in the region where the gravity of the Sun the planet is orbiting around and the gravity of the planet are comparable.

None of these are simple calculations, and all of them require a lot more information than just mass of planet, initial asteroid velocity and distance, and minimal distance on the flyby.

• @jumpjack a gravity assist can speed up or slow down an object relative to another body (i.e., the sun) May 19, 2022 at 11:26
• If I understand correctly, the "full" sentence is: "gravity assist of object A around object B can speedup/slowdown object A only w.r.t. object C", right? May 19, 2022 at 11:31
• @jumpjack With respect to the planet or moon that provides an object a gravity assist, all that the interaction does is to change the object's direction. The speed at entry into / exist from the planet's (or moon's) sphere of influence remains unchanged from the perspective of the planet (or moon). From a Sun-centric perspective, this can indeed result in a change in speed as well as a change of direction. May 19, 2022 at 11:31
• The big problem with using the Moon to assist in your capture is that, if you don't do anything else afterwards, your asteroid's new orbit still gets very close to the Moon's orbit, giving the Moon the opportunity to change the orbit again, and again when they have future close approaches, until you move it to avoid this, or a Lunar flyby kicks the asteroid back into interplanetary space, (or, with a small chance, into the Earth or the Moon) May 19, 2022 at 13:20
• @BrendanLuke15 I think DeltaV for redirecting it heavily depends on distance from Earth at the moment of redirection: you could need pushing away by 1cm or 1km depending on such distance. May 19, 2022 at 13:51