The first drop in the asteroid-moving bucket

 kw: science, orbital mechanics, asteroids, near-earth asteroids, dart mission

Didymos is a small asteroid, about 3/4 km in diameter, or less than half a mile. Not quite mountain-sized, more like a big hill. It has a satellite, named Dimorphos, 170m in diameter, the size of a five-story office building. Unlike an office building, which is 90+% air, it is a big rock. It weighs about five million tons.

This orbiting pair have the great good fortune to be in an orbit that is "reachable" by spacecraft. Not quite Earth-crossing, but much closer than most. As an orbiting pair, these rocks are also much easier to study dynamically. In particular, the orbit of Dimorphos about its common center of gravity with Didymos can be well-characterized, and very small changes in its orbit can be detected. Changes such as the one that will soon occur.

In a couple of weeks, a NASA spacecraft will be smashed into Dimorphos at high speed, and the collision will be watched by a companion spacecraft (the little one shown at center left in this NASA publicity image); and also from ground-based telescopes, symbolized by the icons at lower left.

How sensitive a "probe" is this little satellite? The key is its orbital velocity and period, which can be measured with great precision.

The collision, on September 26, 2022, will be made on the leading side, so it will slow Dimorphos down a tiny bit, moving it into an orbit just a bit closer to Didymos. The key parameters are these:

• Mass of Dimorphos: 4.8 billion kg, equal to 4.8 million metric tons or 5.3 million short tons.
• Mass of the DART impactor: about 500 kg on impact. It starts out weighing 610 kg, and burns propellant to ramp up to speed.
• Impact relative velocity: 6.6 km/sec, equal to 4.1 mi/sec or almost 15,000 mph. For comparison, the orbital velocity of Earth around the Sun is about 67,000 mph or 29.9 km/sec.

The minimum change in the velocity of Dimorphos is calculated by assuming a perfectly inelastic collision. It comes to 0.6875 mm/sec. 

NASA writes that they expect an orbital velocity change of 0.4 mm/sec; perhaps they are assuming lots of kinetic energy will be lost to vaporizing the DART impactor and about a desk-sized chunk of Dimorphos. NASA expects this small slowing of the moonlet to move it into a slightly smaller orbit, such that it will speed up a bit and each orbit will take about 10 minutes less than before. The orbital period is presently just under 12 hours.

It occurs to me that NASA's figure of 0.4 mm/sec must represent the expected increase in orbital velocity resulting from the shrinking of the orbit. Perhaps the instantaneous "bump" will be of the order of 0.7 mm/sec of slowing, but in the resulting, smaller orbit, Dimorphos will have an average velocity as NASA has calculated (their math whizzes are certainly much more savvy than I!).

That's as far as my amateurish figurations can take me. I'll stay tuned to the NASA webcast on the 26th! This is step 1 in figuring out what it takes to shift the orbit of any asteroid that is found to be threatening Earth.