I can’t wrap my mind around why you need to be going a certain speed to escape the pull from earth’s gravity.
In my mind I envision 5 people playing tug of war with a bull. The people are exerting a pulling force but the bull would be able to overcome it. Let’s say the humans never get tired but the bull will be able to exceed the forces pulling it back and continue to move forward. That can happen at 22mph or 2mph.
Outside of it being severely inefficient (I’m guessing), why can’t an object just travel upwards at low speeds and eventually overcome the pull of the earth because it has lots of… torque (for lack of a better word)?
In: Physics
Gravitational potential energy is the reason.
Let’s set the zero point of potential energy to be an infinite distance from Earth.
U=-GMm/r is our formula for gravitational potential energy. The closer you are to the mass (Earth), the less potential energy you have.
What happens if we have enough kinetic energy that we can still have some leftover when we bring our potential energy to zero?
KE + U = 0 is the bare minimum amount of energy it takes to come to a stop at r=infinity. This is where we find escape velocity
1/2mv^2 – GMm/r = 0
1/2mv^2 = GMm/r
1/2v^2 = GM/r
v^2 = 2GM/r
v = sqrt(2GM/r) is our escape velocity (r being our current distance from the center of the Earth)
If we plug in values for Earth, at Earth’s surface, escape velocity is about 11.2 km/s.
That means if right now, you started moving 11.2 km/s in any direction (and didn’t hit anything) you would keep moving away from Earth forever because you have more energy than the Earth’s gravitational pull binds you.
When we launch spaceships to leave the Earth system, we put them into orbit first because going that fast in the atmosphere is not feasible and would vaporize basically everything anywhere near the spacecraft, and because burning our rockets straight up until we reach escaoe velocity is less efficient because gravity is always working against us. By going sideways, the gravity of Earth isn’t fighting us the whole way.
It’s like we are in a valley with the Earth at the center, and you can shoot yourself out, but if you don’t have enough speed to get over the edge, you will inevitably fall back into the valley.
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