Gravity what holds us on the earth?

[b.j.c]

This is probably a stupid question, but anyway...

If you calculate the force of gravity between the Earth and a, say, 70.0kg person, it comes out about 688N.

Now, we are spinning with the Earth and at the surface of the equator the speed is about 1669km/hr. If you calculate the centripetal force required to keep a 70.0kg person rotating in a fixed orbit (radius of earth) at 1669km/hr you will find it comes out around 3e7N.

So it would seem that we should just go flying off the planet because gravity cannot supply the centripetal force required to keep us orbiting with the same radius. How do we stay on the ground then? What have I missed?

 

[James R]

Your centripetal force is wrong. The force required on a 70 kg person is only 2.4 N. Gravity supplies 688 N, which is more than enough to keep the person on the ground.

 

[b.j.c]

Thanks James, a very dumb mistake.

So the 'leftover' force goes into accelerating us toward the Earth if we jump or something?

 

[James R]

Yes. The leftover force is what pulls you down again when you jump up, or fall off something high.

 

[b.j.c]

Cool, thanks.