Will the object spin as the earth spins?

If an object is designed to levitate a few kilometers above the ground, and the point directly below the object on earth is called $A$, as time passes and the earth rotates about its axis, will the object still lie directly above point $A$ (at an angle of 90) as it originally did or will they both move out of line with each other?

• How does this "levitation" work? Is it using the atmosphere and trying to be motionless in the air? – BowlOfRed Oct 16 '15 at 19:40
• it could work like a hovercraft or a hot air balloon. Could be a helicopter too – user140161 Oct 16 '15 at 19:45
• – BowlOfRed Oct 16 '15 at 19:50
• this is related but still leaves me confused because I'm assuming an airless earth – user140161 Oct 16 '15 at 19:54
• The answer actually does depend on the engineering of the vehicle, since any thrust based approach would necessarily rotate along with the Earth - otherwise the thrust doesn't consistently oppose the gravity. – Asher Oct 16 '15 at 21:11

There are a lot of assumptions which I am forced to make here because you have not specified anything.

If the earth is airless (i.e without an atmosphere) and you project an object perpendicularly which was initially at rest on the earth's surface and will levitate itself in the air (say using rockets), then the object will rotate along with the earth and always stay above the point A, as specified in your question. This is because it was initially rotating along with the earth at point A and nothing is preventing it from doing so above A.

If you project the object with some initial velocity in some other direction apart from the vertical, it will obviously appear to move away as seen from point A.

If there is no atmosphere, none among the hovercraft, hot air balloon and the helicopter would work in levitating themselves.

• it was rotating while on earth because it was in contact with the earth. Why would it rotate the same way while above the earth? – user140161 Oct 16 '15 at 21:25