# Problem: An object of mass m is launched from a planet of mass M and radius R.Part (a) Derive an expression for the minimum launch speed needed for the object to escape gravity (meaning the object to reach r = ∞)Part (b) Calculate this minimum launch speed (called the escape velocity) in m/s for a planet of mass M = 7x1027 kg and R = 85x104 km

###### FREE Expert Solution

Escape velocity is defined as the minimum launch speed for an object to escape.

This means that the object stops very far away and never returns to the planet.

Force of gravity is given by:

$\overline{){{\mathbf{F}}}_{{\mathbf{G}}}{\mathbf{=}}\frac{\mathbf{G}\mathbf{M}\mathbf{m}}{{\mathbf{r}}^{\mathbf{2}}}}$

When r is infinity, FG = 0

When the object stops far away, vf = 0

96% (244 ratings) ###### Problem Details

An object of mass m is launched from a planet of mass M and radius R.

Part (a) Derive an expression for the minimum launch speed needed for the object to escape gravity (meaning the object to reach r = ∞)

Part (b) Calculate this minimum launch speed (called the escape velocity) in m/s for a planet of mass M = 7x1027 kg and R = 85x104 km

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