Treetop Orbit?

Question

If the earth had no air (atmosphere) or mountains to interfere, could a satellite given adequate initial velocity orbit arbitraitly close to the earth's surface -- provided it did not touch?

a) Yes, it could.

b) No, orbits are only possible at a sufficient distance above the earth's surface where gravitation is reduced.

The answer is: a. It is important to realize that a satellite is simply a freely falling body that has enough tangential or sideways speed to enable it to fall around the earth raher than into it. If a projectile is launched horizontally at treetop level at everyday speeds, its curved path would quickly intercept the earth and it would crash. But if it were launched at 5 miles per second (18000 mph) its curved path would match the curvature of the earth's surface. If no obstructions or air resistance were present, it would continuously fall without intercepting the earth -- it would be in circular orbit. If it were projected at higher speeds it would follow elliptically-shaped orbits -- at projection speeds beyond 7 miles per second (25000 mph) would escape the earth altogether. So the eseence of launching satellites is to get them up above air drag and boost their tangential speeds high enough so that the curvature of their paths at least matches the curvature of the earth.

A satellite could not only orbit at treetop level (providing it encountered no atmosphere, mountains, or other obstructions), it could orbit the earth in a tunnel below the earth's surface, providing all the air was removed from the tunnel so there would be no drag on the satellite.

Question: Would its speed in such a tunnel be greater or less than 5 miles per second?

Linlyons is correct on two counts -- his analysis is correct and his intended compliment to both jgoulden and to aurum was misunderstood, unfortunately....

Thank you Linlyons for your usual panache in providing both a terrific answer and a graceful response.

Answer 1

If it was rotating along the plane the equator creates, then sure it could. It would obviously need a much greater initial velocity though.

Edit: linlyons. . . If a satellite orbits closer to a planet, a higher velocity is needed. I made no mention of necessary energy. Don't try to be condescending to make yourself look better if you're wrong.

Answer 2

Neither answer is correct, but (a) is more correct than (b). If the Earth were a perfect sphere with radially symmetric density, (a) would be completely correct. Alas, the Earth is NOT a perfect uniform sphere and minor gravitational anomolies would prevent an arbitrarily close orbit.