# The most distant object that can still orbit the Earth.

1. Dec 11, 2008

### pixel01

Hi all,

I am puzzled as to how far an object can still be influenced by the Earth gravity.
The same question with the Sun as the central object.

Thank you.

2. Dec 11, 2008

Staff Emeritus
An object is affected by Earth's gravity forever. However, the radius of orbiting depends on how strong the pull of other objects is, and that depends on exactly where the object in question is. There is no single "how far" answer.

3. Dec 11, 2008

### tiny-tim

Suppose you launched something from Earth, almost directly towards the Sun, so that it just looped round the Sun and came back … would it come back to the Earth?

How far from the Earth, towards the Sun, could it get without getting lost?

4. Dec 11, 2008

### pixel01

OK, so let's suppose the Earth is somewhere else that has no interferences like Jupiter or Mars etc... (and no Sun). Can there be an object orbiting the 'Earth' from as far as Pluto?

5. Dec 11, 2008

### D H

Staff Emeritus
Yes. Gravity goes on forever; it just dwindles as 1/r2. If there were no other massive bodies nearby, an object much, much further from the Earth than Pluto could still be in orbit around the Earth. Eventually you would have to add in expansion of space as an interfering "force". The reason we don't see objects as far away as Pluto orbiting the Earth is because of all those other objects in the Solar System, not because Earth's gravity ends at some point.

6. Dec 11, 2008

### tony873004

The only relavant perturbers for Earth satellites are the Sun and the Moon. The planets are insignificant compared to them.

The maximum distance an object can orbit Earth is about 1.5 million kilometers. This is the edge of the Earth's Hill Sphere. An object there needs to be orbiting retrograde (the opposite direction Earth orbits the Sun). At best, it will complete a few orbits before escaping Earth. This assumes the Moon does not exist.

Interior to this, things become stable quickly. Their orbits will be chaotic, but they will remain bound to Earth, indefinately if they are within 2/3 of the edge of Earth's Hill Sphere.

Prograde objects are not as stable. They can only orbit about halfway to the edge of Earth's Hill Sphere before being stripped away by the Sun. This also assumes the Moon does not exist.

If you consider the Moon as part of the system, there are no stable prograde orbits external to the Moon's orbit. The Moon will perturb all objects until they escape Earth or collide with Earth or Moon. But the Moon's influence on retrograde objects is not that large, so you can orbit retrograde out to about 1 million km.

Objects are slightly more stable in June than in January. That is because Earth is closer to the Sun in January, which shrinks its Hill Sphere. Over long periods of time, Earth's eccentricity oscillates from nearly circular to about twice as elliptical as its current value. During periods when the eccentricity is at its maximum, the Hill Sphere shrinks even further during Earth's perihelion. The planets, and primarily Jupiter, are what cause Earth's eccentricity to oscillate. So this gets the planets an honorable mention in destabalizing Earth satellites.

The OP asked about the maximum distance something can orbit the Sun. Currently, Alpha Centauri sets the limit of the Sun's Hill Sphere. Without running the numbers, I believe it's about 1.5 light years. The Galactic Tide sets a maximum even if there are no other stars currently near the Sun. Again, without running the numbers, I believe it's about 2-3 light years.

**edit:
I ran the numbers. Because of Alpha Centauri, the Sun's Hill Sphere is about 2.4 light years. If Alpha Centauri were not present, the maximum the Sun's Hill Sphere could be is about 4 light years, limited by the Galactic Tide.