What is Escape Velocity?
Sure, you can look up the equation for escape velocity, but what does it really mean?
Let’s start with the most conceptual idea possible. Suppose you have a ball and you toss it straight up into the air. As the ball rises, it decreases in speed until it reaches its highest point. After that, it starts moving back down and increasing in speed. That’s something we have all probably experienced (throwing a ball).
The faster you throw a ball (on the surface of the Earth) the higher it will go — that is probably obvious. However, what’s not so obvious is that if you get a ball going fast enough (ignoring air resistance) then it will NEVER COME BACK DOWN. This velocity is the escape velocity.
See. That wasn’t so bad. The end. Just kidding.
Velocity vs. Position on the Surface of the Earth
In order to get a more mathematical explanation of escape velocity, I want to model the motion of a ball near the surface of the Earth. By “near” I mean within 5000 meters from the ground (approximately). What happens if I toss the ball (1 kg) straight up with a velocity v0 = 10 m/s?
I am going to create a numerical model of this motion — even though we could solve this problem with some basic kinematics. But by using a numerical calculation I can set stuff up for a more complicated problem that…
