# How long does it take for an asteroid to get to Earth?

How long does it take an asteroid to get from the asteroid belt, to Earth? I know the asteroids don't go directly from the asteroid belt to Earth, but I know it's not quick, either. The time probably varies, but what's the average time?

• A year or two... very roughly
– uhoh
Jun 26 '19 at 10:16
• You can get a rough estimate for things like that by computing a Hohmann transfer orbit. Jun 26 '19 at 10:46

The full orbital period of an object orbiting the sun is $$T=2\pi \sqrt{\frac{a^3}{GM_\odot}},$$ where $$a$$ is the semi-major axis of the orbit and $$M_\odot$$ the mass of the sun.
If the asteroid has apoapsis in the asteroid belt ($$r_{max}= 3$$ AU) and periapsis near Earth ($$r_{min}=1$$ AU) then the semimajor axis will be $$a=(r_{max}+r_{min})/2=2$$ AU and going in from the belt takes half a period, so the answer is $$\pi\sqrt{(2 AU)^3/GM_\odot}=1.4140$$ years. An asteroid coming from further out, say 4 AU, would take 1.9762 years. From 2 AU, 0.9184 years.
However, it is worth noting that long-periodic comets can move fast (tens of km/s). Such a comet (or an interstellar asteroid) would have a velocity on the order of $$\sqrt{2GM_\odot/(1AU)}\approx 42.1285$$ km/s if it came in from the outer edge of the solar system. That would cross the 2 AU from the asteroid belt to Earth in about 82 days.