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
Gravity will always slow you down, even at very large distances (though it will be much weaker then).
If you start with a certain velocity from the surface of earth (and cannot accelerate further), you will get slower and slower over time. If your initial velocity was too low then you will stop at some point and change directions, and then fall back towards earth.
Only if you have the escape velocity or higher, you have enough energy to overcome (escape) the gravity completely and you will never be stopped by the earth gravity.
However that is only important if you have something that starts with a constant velocity at earth and can not accelerate by itself. If you have something like a rocket, which can accelerate by itself, then escape velocity you don’t necessarily need escape velocity initially (however building a rocket that can accelerate in space for long times is also not easy).
You don’t. Escape velocity only applies to ballistic launches, where the object you’re launching has no propulsion of its own and has to get all of its speed *at launch*. Shoot a cannon ball out of a cannon, and you know that when the ball leaves the cannon it has to be traveling faster than Earth’s escape velocity, or it will come crashing back to Earth.
Launch a rocket, however, and the concept of escape velocity becomes moot. As you said, you can, in principle, fly up at an absolute snail’s pace, and as long as you keep flying up, you will eventually make it to space. It’s just (again, as you said), rather inefficient to do it that way, because every second you spend in Earth’s gravity is a second that this gravity saps away your speed.
I think you just misunderstood what escape velocity means. It’s the speed you’d have to throw a thing up **from the surface, with no thrust after that**, for it to be able to leave.
It’s the required launch speed for things with no thrust of their own.
It does NOT mean “you must be going this fast to escape”. It must means if you have no thrust you have to leave the surface this fast or you’ll fall back down.
But just like you suspect, if you have thrust, there is no minimum speed needed to escape. A rocket can ascend while going 1 mph the entire time, no problem.
Escape velocity only applies to unpowered objects. Just as you say, a rocket could just keep going at low speeds and eventually overcome the pull of the Earth, as long as it had enough fuel to keep burning that long. But that fuel requirement is a very big *if*: fuel adds weight, which makes the rocket harder to launch.
Escape velocity is the way around this problem. Once a rocket hits escape velocity, it doesn’t need fuel to keep going, so it doesn’t need to carry any more fuel than needed to reach escape velocity in the first place (and maybe a little more for maneuvering). This allows the rocket to be lighter, which makes it easier to launch.
You first have to get above the atmosphere which always acts as a brake… you need to get to a certain velocity to escape the atmosphere and enter a freefall orbit around the earth, or in a ‘straight’ line away from earth without risk of falling back when the fuel runs out.
Hence escape velocity.
You need to be moving fast enough to get away from the drag of atmosphere and to enough speed before the fuel runs out and gravity takes control again.
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.
> Outside of it being severely inefficient (I’m guessing)
Your guess is correct, it’s very inefficient so with current rocket technology if you tried to go up slowly you would run out of fuel before getting far enough away from Earth, and would just fall back
Instead you go up as quickly as possible to reduce the amount of gravity pulling you down as quickly as possible. Once you’re going faster than escape velocity the engine can be shut down and you coast the rest of the way away from Earth.
You’ve actually got pretty close to it: gravity at Earth’s surface is approximately 10m/s2. This means, anything travelling directly away from Earth needs to accelerate 10 metres per second, every second, to escape the pull of Earth: any slower, and the pull from Earth will slow you down, and if you drop below that critical velocity before moving far enough away from Earth, you will eventually be pulled back.
Rather than your bull tug of war, let’s instead imagine a cable drum with a rope that you are attached to. This drum winds in 10 meters of rope every second, but speeds up the more you pull out. If you pull on the other end, the rate slows. In this scenario, if you pulled at a rate of 10 meters per second to start with, you would stay in the same place; if you pull faster, you will start to move away, but the further you move away, the harder you have to pull as the drum speeds up. If you manage to fully unwind the rope, you can untie it, and you are free to move your own way.
Before people come at me, this is an incredibly simplified version, I know there are other variables to consider; but this is “Explain Like I’m 5”, not “give me a master’s discourse”.
There is one thing that you don’t take into the account. The bull’s strength is lower the further you are from said bull. And it falls with the _square_ of the distance. So if you get 2 times further from the bull, it pulls you 4 times weaker. This is according to the Newton’s law of gravitation, which uses inverse square.
The force that the bull exerts slows you down linearly. So after you travel 2 times further, you are losing speed with a 4 times lower ratio. There exists an initial speed where you only reach 0 speed once you travel to infinity (we need calculus to calculate this rigorously). This speed is called escape velocity.
Imagine you throw a rock. You want it to fly far enough to fall farther than earth so that it doesn’t fall black on earth but “behind” it.
How fast do you have to throw that rock to make it fly far enough ? That’s your escape velocity.
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