<p>The full orbital period of an object orbiting the sun is <span class="math-container">$$T=2\pi \sqrt{\frac{a^3}{GM_\odot}},$$</span> where <span class="math-container">$a$</span> is the semi-major axis of the orbit and <span class="math-container">$M_\odot$</span> the mass of the sun. </p>

<p>If the asteroid has apoapsis in the asteroid belt (<span class="math-container">$r_{max}= 3$</span> AU) and periapsis near Earth (<span class="math-container">$r_{min}=1$</span> AU) then the semimajor axis will be <span class="math-container">$a=(r_{max}+r_{min})/2=2$</span> AU and going in from the belt takes half a period, so the answer is <span class="math-container">$\pi\sqrt{(2 AU)^3/GM_\odot}=1.4140$</span> years. An asteroid coming from further out, say 4 AU, would take 1.9762 years. From 2 AU, 0.9184 years.</p>

<p>Of course, were one to just give an asteroid a big push it could move nearly arbitrarily fast (up to the lightspeed limit if we want to be absurd) along an Earth-intersecting orbit, but I suspect the question was about normal asteroids. </p>

<p>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 <span class="math-container">$\sqrt{2GM_\odot/(1AU)}\approx 42.1285$</span> 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. </p>

CC BY-SA 4.0
2019-06-26T16:03:03.910Z
If you're thinking of asteroids which hit Earth "naturally", it is very unlikely that they get displaced from a stable orbit in the asteroid belt onto  a collision course with Earth.  It's much more likely that they get displaced onto an "Earth-crossining" orbit and then remain in it for millions of years, before they happen to actually collide with Earth.
Steve Linton
CC BY-SA 4.0
2019-06-26T15:59:06.977Z
2019-06-26T15:59:06.977Z
Anders Sandberg
<p>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?</p>

CC BY-SA 4.0
2019-06-26T10:16:11.467Z
A year or two... very roughly
uhoh
CC BY-SA 4.0
2019-06-26T10:46:06.107Z
You can get a rough estimate for things like that by computing a [Hohmann transfer orbit](https://en.wikipedia.org/wiki/Hohmann_transfer_orbit).
PM 2Ring
<asteroids><asteroid-belt>
How long does it take for an asteroid to get to Earth?
GoingFTL
# How long does it take for an asteroid to get to Earth?

(Asked by: username_0 on 2019-06-26)

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?

**Tags:** asteroids, asteroid-belt

> **Comments:**
> **username_1**: A year or two... very roughly  
> **username_2**: You can get a rough estimate for things like that by computing a [Hohmann transfer orbit](https://en.wikipedia.org/wiki/Hohmann_transfer_orbit).  

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## 1 answers

### Answer by username_3 on 2019-06-26. Score: 4

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.

Of course, were one to just give an asteroid a big push it could move nearly arbitrarily fast (up to the lightspeed limit if we want to be absurd) along an Earth-intersecting orbit, but I suspect the question was about normal asteroids.

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.

> **Comments:**
> **username_4**: If you're thinking of asteroids which hit Earth "naturally", it is very unlikely that they get displaced from a stable orbit in the asteroid belt onto  a collision course with Earth.  It's much more likely that they get displaced onto an "Earth-crossining" orbit and then remain in it for millions of years, before they happen to actually collide with Earth.  

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