Question

Scotty finds it difficult to play catch on planet Apgar because the planet'sescape speed is only 5.00 m/s, and if Scotty throws the ball too hard, it fliesaway. If planet Apgar has a mass of 1.56 X 1015 kg, what is its radius?

Answer 1

We remember that the escape velocity formula is given by:

$v=\sqrt{\frac{2Gm}{r}}$

Now, from this we determine the radius as follows:

$v^2=\frac{2Gm}{r}\Rightarrow r=\frac{2Gm}{v^2}$

Then:

$r=\frac{2(6.67\ast10^{-11})(1.56\ast10^{15})}{(5)^2}\Rightarrow r=8324.16m$

So, the radius of "planet" Apgar is approximately 8324.16 meters.