a 70 kg block rests on the earth's surface. How much energy is required to move the block very far from the earth, ending up at rest again?

Answer 1

Using conservation of energy
Efinal=Einitial + Work

Neglecting rest mass energies
Uf+Kf=Ui+Ki+W

Starting and ending at rest so
Kf=Ki=0

Therefore
W=Uf-Ui

Using Gravitational potential energy
U=-Gm1m2/r

When r is very large
Uf=0

So
W=Gm1m2/r