Time for Free Fall from Great Distances

[Thecla]

The equations of a falling object dropped from a 1000 foot tall building are simple:

eq 1 $s=1/2( at^2)$

eq 2 $v(final)=(2as)^.5$

eq 3 $v(final)=at$

where a is the acceleration due to gravity at the surface of the earth
s is the height of the building, t is the time it takes to fall

If we dropped an object from 5000 miles in space we can't use these formulae because the acceleration initially is smaller, gradually increasing to the value ,a, at the surface of the earth.

Are there simple formula that relate the distance fallen to time,eq 1; the final velocity to distance eq 2 and the final velocity to time eq3 that do not involve integrals or differential equations, just simple algebra

 

[Dale]

You could get velocity at a given distance by using the conservation of energy. No calculus, just algebra. But I don’t know how to get the time without it.

 

[Thecla]

Thanks