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.
Latest Answers