Why is there a velocity associated with escaping from earth’s atmosphere? If an object were to fly from the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
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You have to be moving fast enough that gravity never pulls you back.
As things get further away, the pull of gravity becomes weaker.
Imagine a slope that starts to level off at the top. You can roll a ball up the slope and have it roll back to you. But if you roll it fast enough, it can make it up to the “top” of the slope and never come back.
Edit. OP was accounting for constant acceleration in their perspective. That’s not something you consider when looking at escape velocity, and I completely overlooked that in my answer.
The object is going up at 1 m/s, and Earth’s gravity is pulling it down at 9.8 m/s/s. You’re going to need a little bit more oomph.
Basically you are trying to overcome the pull of gravity, an orbit is going fast enough not to fall back down to Earth by having enough horizontal velocity to keep missing the Earth as gravity pulls you back down escape velocity means that you are moving fast enough not to fall back down.
You forget you’re on an object which is spinning and that momentum stays with you when you take off
There is no such thing as “going straight up”
True. But that isn’t what escape velocity means. The escape velocity (at ground level) is the speed an object must be travelling at ground level going upwards WITHOUT FURTHER BOOST.
For a vehicle to travel 1m/s constantly against gravity, energy must be added ie there needs to be some form of boost or thrust (or it will slow down and fall back to earth). In that circumstance, there is no need to refer to the escape velocity.
>the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
If there’s no change in acceleration you are constantly putting energy into the system to counteract gravity. When we talk escape velocity we are essentially talking if you were launched into space at a start velocity. Why do we think this way? Well your rocket has a limited amount of fuel, and thus energy. So you want to calculate so you have (at least) enough fuel to escape gravity.
The way to think about it is to think about energy instead of velocity.
Being on the ground you have what we call a negative potential energy. You need to put in energy to be in a neutral state. The reason its negative is because the reference frame would be your state where you are infinitely far away from the object and thus not effected by its gravity.
The energy is defined as 1/m * intregal from x to inf of G*m*M/(x^2)
G is the universal gravity constant, x is the height from the center of the object(Height from center of earth in this case), m is your mass and M is the mass of the earth in this case.
You get some massive amount of negative energy. In order to completely escape this, you need a kinetic energy equal to that potential energy. Kinetic energy is calculated by e=1/2 * m * v^2.
You take these two equations and solve for v, and get:
v_esc = sqrt(2*G*m/x)
You can get input your current height from center of earth, G and mass of earth to get the escape velocity.
> In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, ***non-propelled object*** to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it.
https://en.wikipedia.org/wiki/Escape_velocity
With atmospheric drag and gravity, it’s impossible for a non-propelled object to actually maintain 1 m/s.
If something were to fly from the surface of the planet at 1 m/s then gravity would pull it back and have it land again in a fraction of a second. If you get something to fly faster from the surface it might take more time but it will still fall down again. You need to get above the atmosphere and then reach orbital velocities to prevent it from falling down to the planet under the force of gravity. But it will still not escape gravity. To get something far away from the planet you need to get in flying away so fast that no matter how long gravity will not be able to pull it back. That is escape velocity.
Escape velocity doesn’t have anything to do with the atmosphere. It’s the speed at which you can escape earth’s gravity well without additional energy.
Getting to space is relatively easy, going straight up you need 1400m/s of velocity to reach 100km of height(ignoring atmospheric drag). Staying in orbit is much harder. At 100km altitude, you need to be going sideways at 7850m/s in order to stay in orbit. Any slower and you just fall right back down.
If you increase that 7.8 km/s to 11.2 km/s, that’s escape velocity, and you’ll leave the earth behind and end up in orbit around the sun.
>If an object were to fly from the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
Yes, it would. If you would constantly travel at 1 m/s, you’d eventually get anywhere.
However, escape velocity is the velocity at which a **non-propelled** objects escapes the gravitational influence of the planet.
In other words, if you had a rocket that has infinite fuel and can constantly fly at 1 m/s, it would eventually fly off.
However, if you launch a cannonball at 1 m/s, it wouldn’t fly very far. If you launch it at escape velocity (and if we neglect atmospheric drag), then it would escape Earths the influence of Earth’s gravity.
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