Isn’t going up with velocity greater than 9.81 m/s be enough to escape earth’s gravity?
In: Physics
11.18 km/s is the *escape velocity* from Earth’s surface. This means that if you launch an object from Earth’s surface at that speed, Earth’s gravity cannot slow it back down to a stop. Gravity will eat away at the object’s speed, initially reducing it by about 9.8 m/s every second. So after one second, the object’s speed is 11.18 km/s minus 9.8 m/s. After two seconds, it’s 11.18 km/s minus 19.6 m/s, etc. At this rate, Earth’s gravity would bring the object to a halt in 1140 seconds. However, the pull of gravity gets weaker as the object travels away from the Earth. At 1000 km, gravity only reduces your speed by about 7.3 m/s every second. At 2000 km, it’s less than 6 m/s per second. Eventually, the pull of Earth’s gravity becomes (nearly) 0. At that point, an object is said to have escaped the Earth’s gravitational influence. If you do the necessary calculations, taking into account how much of your speed Earth eats away as you climb, you find that you need to start with a speed of about 11.18 km/s in order to make it to this escape point.
However, this only applies to objects that don’t have their own propulsion system. Without propulsion, the launched object needs to get all its acceleration at take-off from the launching system (e.g. a cannon). An object like that needs to be accelerated all the way to 11.18 km/s in order to eventually escape Earth’s gravity. A rocket, on the other hand, can keep pushing itself up while Earth is pulling down on it. In principle, a rocket could escape Earth while never flying faster than the interstate speed limit, if it just keeps pushing to compensate for Earth’s pull. So, the notion of escape velocity doesn’t strictly apply to self-propelled objects like rockets.
In practice, though, it’s a good idea to accelerate the rocket as much as possible in the beginning of its flight, rather than later on. The reason being that the rocket has to carry its own fuel. The more fuel it’s carrying, the heavier it is, and the more energy it takes to push the rocket upwards. So it turns out to be more efficient to spend your fuel as quickly as possible, so that the rocket quickly gets lighter, and pushing quickly gets easier. So in practice, a rocket will actually try to reach a speed close to (or beyond) Earth’s escape velocity early on in its launch trajectory.
You’re mixing up velocity and acceleration.
The acceleration due to gravity is 9.81 m/s**^2**
Theoretically, any speed above 0 and you could get into space if you kept it up. However, due to the fact that gravity is constantly pulling you down, you need to be putting work in constantly to counteract gravity and keep going up.
Rockets don’t need to fly at speed greater than escape velocity unless they’re going into interplanetary space.
They do need to have enough fuel to achieve a theoretical change in velocity significantly greater than orbital velocity, as some will be used to increase altitude and some will be lost to atmospheric and gravitational drag.
9.81 m/s² is earth’s gravitational pull at the surface: Every second, the a free falling object accelerates by 9.81 m/s. That is why the unit is meters per second *per second*, not just meters per second.
So each second the spaceship is flying away from earth, it loses some speed. This value drops off as the spaceship moves away from earth, eventually becoming so small that the spaceship is affected stronger by the gravity of the sun than the earth – it is now no longer in earth orbit, but in sun orbit, from where it can move to other planets.
Escape velocity is the speed at which the spaceship is moving fast enough to reach that point without falling back to earth – if the spaceship is shot by a cannon from the surface. Real spaceships however fly in orbits around earth, which makes this a lot more complicated.
If you haven’t heard about it, there’s a great game called Kerbal Space Program, which has a pretty good simulation for orbital mechanics. If you’re interested in the topic, I recommend checking the game out on YouTube.
Escape velocity is the initial velocity a *projectile* would need to escape from the gravity well of an object without any further action, and ignoring things like air resistance.
With rockets you need to have enough energy to generate Delta-V (change in velocity) equal to the escape velocity over the course of the launch (allowing for additional fuel to overcome air resistance and other losses) but the rocket itself won’t reach anywhere near that velocity at any point during the launch as a lot of the energy is going straight to overcoming gravity.
Once in space it might get accelerated past that speed if it’s a probe intended to travel long distances, to do this it will have substantial additional fuel to accelerate once in space.
Rockets need to be able to create enough thrust FORCE to beat gravity and lift themselves off the ground. If the rocket needs to reach an orbit out there for delivering a satellite, or leave the Earth’s vicinity completely, then the rocket’s speed needs to eventually be bigger than escape velocity.
The issue is that the rocket’s fuel runs out, so, to escape, the rocket needs to be at faster-than-escape-velocity by the time its rocket engine turns off, or the Earth’s gravity will pull it back to the ground (a rocket with no fuel is like a rock, heh).
* 9.8 m/s^(2) is the acceleration produced by the force of earth’s gravity. It is not a velocity. Rockets have to produce sufficient force in the opposite direction to overcome that velocity, regardless of what speed they wind up going.
* Rockets don’t have to exceed escape velocity to escape the earth. Escape velocity applies to ballistic objects (like a cannonball), not objects that are constantly applying force.
Let’s do it with a rock first. Just drop it. See how long that took?
Now throw it towards the horizon as hard as you can. See how far it went horizontally and how long it took to fall to the ground?
Now we all know the earth is round. The idea is to throw that rock hard enough and far enough so that it goes past the curve of the earth before it lands. This way it never touches the ground again.
We don’t have the means to accelerate stuff quickly enough to launch into orbit at that flat of an angle and achieve high enough speeds. Air is a problem because at those speeds it causes lots of heat and drag so we have to throw it “over” the air. That’s why orbit needs to be out of the atmosphere to stay in orbit.
My take on it anyway.
Rockets don’t need to fly at that speed. Escape velocity is the speed you need to achieve *with no further input.*
So if your rocket was loaded onto a catapult, and simply flung into the air, it’d need to hit escape velocity to escape earth’s gravity.
If it had ‘super duper efficient light space fuel’ and could fire a rocket virtually forever, then it could escape going at 1 foot per hour.
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