Calculating the required energy for throwing a tennis ball into space

[robotleckie]

hello

i would really like to figure out the amount of energy one would reuqire to throw a tennis ball into space hypothetically speaking? i understand that this is impossible but i would like to find out anyway. i would be very grateful if anybody could help me with this.

thankyou

 

[Hootenanny]

If we are ignoring drag, the the problem is rather elementary, just a simple conservation of energy problem. However, if we wish to include drag; then the situation is somewhat more complex.

 

[Janus]

If by "into space", you mean such that it doesn't fall back to Earth, then one way is to find the escape velocity from the Earth,

$$v= \sqrt \frac{2GM}{r}$$
where
G = the gravitational constant
M = the mass of the Earth
r = the radius of the Earth

and then determine the amount of energy that it would take to get your tennis ball up to that speed,

$$E= \frac{mv^2}{2}$$

where
m = the mass of the tennis ball.

This is ignoring atmospheric drag.

 

[robotleckie]

thankyou

hello

thankyou very much, this is very helpful. being a real novice could i ask you what the units of E, m and v are in the second equation? and also, how would could find out the amount of energy required to throw the ball into orbit rather than away from earth? thankyou again.

 

[Janus]

hello

thankyou very much, this is very helpful. being a real novice could i ask you what the units of E, m and v are in the second equation? and also, how would could find out the amount of energy required to throw the ball into orbit rather than away from earth? thankyou again.

They should be the same as in the first equation. They could be ergs, grams and centimeters/sec or joules, kilograms and meters/sec, Just be consistent with which set you use.

As for throwing a tennis ball into orbit, it depends on the orbit. If you could ignore air resistance and irregularities in the surface of the Earth (mountains, etc), you could get an object into orbit around the Earth, just above its surface, with a velocity of somewhere around 7900 meters per sec. If you throw it harder it will rise higher, but it will still return to where you threw it from. To get it into an orbit that does not return to the point where it started, you would have to give it another additional amopunt of speed at some point after it has left your hand. (the best point would be at the furthest point of its orbit.)