If you stand on the surface of a spherical asteroid of mass 1.12*10^17 kg and radius 20km, how fast must you throw a baseball to put it into orbit at 1.0 m above the surface?
GMm/r^2 = 1/2mv^2
G = 6,67*10^-11
The Attempt at a Solution
I rearranged the above equation to get the equation for orbital velocity..
Vorbital = sqrt (2GM/r)
Plugged in the numbers
sqrt((2*6.67*10^-11)*(1.12*10^17)/(20000 + 1))
With that, I got 27.3 m/s which doesn't seem completely out there. The problem is the question has the answer listed as 19.3 m/s
I could not figure it out, but after some playing around realized that 19.3 is the answer if the equation is sqrt(GM/r).
Am I using the wrong equation? How does the equation work if there is no 2? I'm so confused. Thanks for any help.