# How long would it take for an apple to fall to the earth

How long would it take for an apple to fall to the Earth if it were as far away as the Moon and how do you calculate that?

And, say the apple appeared out of nowhere stationary (relative to the Sun) at that distance, would the movement of the Earth leave the apple behind or would the apple follow?

Gold Member
How long would it take for an apple to fall to the Earth if it were as far away as the Moon and how do you calculate that?

The force of gravity on an object is $$F=\frac{Gm_1m_2}{r^2}$$
The force will vary as it comes near the Earth, so you would need Calculus.
If you know the force, you know the acceleration,then you can use the SUVAT equations

QuantumPion
Gold Member
And, say the apple appeared out of nowhere stationary (relative to the Sun) at that distance, would the movement of the Earth leave the apple behind or would the apple follow?

An apple stationary with respect to the sun at the distance of the moon would have a speed relative to the earth equal to earth's orbital speed (30 km/s) which is in far excess of escape velocity. Therefore the apple would fall into the sun and not the earth.

An apple stationary with respect to the sun at the distance of the moon would have a speed relative to the earth equal to earth's orbital speed (30 km/s) which is in far excess of escape velocity. Therefore the apple would fall into the sun and not the earth.

Depends on the angle relative to the earth of where the apple is.

D H
Staff Emeritus