I don't know if it is a good idea to post this, but I just feel like
First of all, you have to know the gravity of all the planets, the
moon, and the sun. I only know that the gravity of the moon is 1/6 g,
which is a sixth of the gravity of earth.
First, let me derive an equation.
V(vertical final) = V(vertical initial) - gt
g = gravitational acceleration t = time
Since the vertical velocity is zero at the top of the trajectory of a
baseball hit by somebody, and I am only talking about half the
V(vertical initial) = gt
I want to know the time the ball takes until it reaches the ground:
t = 2 (V(vertical initial))/g
I want to know the horizontal distance the ball takes on our planet.
Horizontal Distance =HD = V(horizontal initial) times time
= 2(V(horizontal initial) V(vertical initial))/g
Now let's assume that Howard Johnson can swing a bat on
any heavenly body so that the initial horizontal velocity and the
initial vertical velocity of the ball hit by him are always the same
as those of a 430 foot homerun he hit a few months ago at Shea Stadium
On the moon, the gravity is a sixth of that of our planet. So:
HD(on the moon) = 2(V(horizontal initial) V(vertical initial)) / (g/6)
=6 (2(V(horizontal initial) V(vertical initial))) / g
= 6 (HD(on earth)) = 6 times 430 feet = 2580 feet
Wow! Easily a new record.
Since I forgot the gravitational acceleration of each planet and the
sun, this is all I can do.
The easiest way to know this is to know that the distance a guy can
hit the ball is inversely proportional to the gravity of the place,
assuming that there is no air friction.
Since I am in hurry, I have to go without double-checking. I think
this is right since I am a physics major.