# Rotational velocity of a planet

I was thinking, the amount of "gravity" a person feels on the surface of a planet is not only dependent on gravity, but also the centripetal force...

For example, if earth spun 17.04 times as fast as it does now (i.e. 1 day = 1.4 hours) then anything on the surface of the earth would essentially be orbiting it, and would feel weightless!

Also, a planet with much more mass than earth could have the same effective gravity at the surface if it had a larger radius or rotational velocity.

The only thing thats a little fuzzy to me is the effects this would have on actually launching things into space. A planet with higher mass and velocity with the same effective gravity on the surface would still make require much more energy to launch a mass into space, right?

Discuss.

A planet with higher mass and velocity with the same effective gravity on the surface would still make require much more energy to launch a mass into space, right?
No. If the force ##F_{gravitational} - F_{centrifugal}## is the same on both planets (at some particular latitudes), than you need the same amount of energy.

Note: in this context I assume that "launching a mass into space" means just to leave the surface for a short instant (to consider a stable orbit or escaping the gravitational field entirely, we would need to work with particular values, including the size of the planet). Next, I also assume that the planet is perfectly spherical and homogeneous, so the (true) gravitational acceleration is the same everywhere on the surface (we are ignoring any effects of the rotation on the structure and shape of the planet).

For example, if earth spun 17.04 times as fast as it does now (i.e. 1 day = 1.4 hours) then anything on the surface of the earth would essentially be orbiting it, and would feel weightless!
Only at the equator (the centrifugal force depends on latitude). As you move further toward any of the pole, the centrifugal effect would diminish and the resulting force would pull objects toward the surface. On the poles, the rotation of the planet doesn't provide any centrifugal force to counteract the gravity.

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