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Physics of converting a spacecraft to an asteroid

There are two things you should be aware of. DART moves backwards after a collision, as it bounced. Because velocity is a vector it means it has negative momentum in this example.

A second aspect of the kinetic equation concerns the squared velocity. DART may have negative velocity, but it has positive kinetic energie.

We just have two equations and two variables, so these equations aren’t impossible to solve—but they’re also not trivial. Let’s see what we would get if we did the math. (If you want the full details, I’ve got you covered.

Illustration: Rhett Allain

These values are DART, Dimorphos and give a final velocity at 1.46 mm/s. It’s double the recoil velocity in an inelastic collision. DART has returned to its original orbit. More Greater change in momentum (going to positive or negative) Dimorphos will experience a greater change in momentum, and velocity. It’s still a tiny change—but twice something tiny is bigger than tiny.

The collision spectrum is not only divided into elastic and inelastic. The majority of collisions are somewhere in-between, with the object not sticking together and the kinetic energy being lost. The calculations show that an elastic collision is the most effective way to alter the orbit of an asteroid.

Images of Dimorphos taken after collision show that at most some debris was ejected by the asteroid. Since the debris moves in the opposite direction of DART’s original motion, it appears that the spacecraft partially bounced back, showing the increase in the change in Dimorphos’ momentum. This is the view you should be looking for if your goal it to move a rock into space. You would get something close to an inelastic collider with a slower asteroid recoil velocity, but without any ejected materials.

What is the best way to measure the impact?

The best case scenario, as you can see in the above example would only change the velocity by 1.34 millimeters per sec. This small change in velocity is very difficult to measure. But Dimorphos has a bonus feature—it’s part of a double asteroid system. Remember, it’s orbiting its bigger partner, Didymos. This is why NASA selected this target. Measurement of the orbital period (the time taken for an object to orbit the Earth) is key to determining the effects of it colliding with Dimorphos. This will allow you to determine if the orbit has changed since the collision.

Dimorphos orbits Didymos using the same physics as the moon orbits Earth. Since there is a gravitational interaction between them, Didymos pulls Dimorphos toward their common center of mass—a point much closer to the center of Didymos, because it’s larger. The gravitational force between them would eventually cause their collision if both of them started at rest. But that’s not the case. Dimorphos instead has a velocity which is mostly parallel to the gravitational force. This causes it to orbit around its center of mass. This orbit could be circular, but it is possible.

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