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{(2Gm)/(r)}`

Now, from this we determine the radius as follows:

`v^2=(2Gm)/(r)\Rightarrow r=(2Gm)/(v^2)`

Then:

`r=(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.