Compute The Escape Velocity Needed To Launch A Rocket From The Surface Of Mars

Why does a rocket need to get to escape velocity to get into space?

The answer is that a rocket doesn’t need to get to escape velocity to reach space. Escape velocity (at the Earth’s surface) is that speed which is required to completely overcome Earth’s gravitational field. You need to reach escape velocity if (say) you want to travel to Mars, but not if you just want to get to the International Space Station.Note that the escape velocity is lower the higher a rocket gets above the Earth’s surface. No rocket will instantly hit escape velocity as it is launched. It will rather speed over time, and by the time it reaches escape velocity that might be somewhat lower than the escape velocity at the Earth’s surface.Space is generally considered to start at about 100km above the Earth’s surface (although that’s a rather arbitrary definition as the, by then, very thin atmosphere continues further). The minimum requirement of a rocket to be considered to have reached space by that definition would be to reach that altitude. The WW II V2 rocket reached almost that altitude and its peak speed was less than 6,000 m/s, or only about 14% of escape velocity.The next step up is to go fast enough to go into orbit, and that’s what is called orbital velocity. If you take the first artificial satellite, Sputnik 1, that had an orbital speed of about 18,000 km/hr, or rather less than half escape velocity.Satellites travelling in higher orbit (such as the geostationary ones occupied by satellite TV broadcasters) have a lower orbital speed, but it may be necessary (depending exactly on how long the “burns” last and the number of stages) for the rocket to achieve a much higher speed than the eventual orbital speed.NB, I should add and answer to your text as well. You are quite right that, in theory, a rocket which could maintain a constant 1 km/s (which is about the maximum speed of a V2 rocket) would eventually break free of Earth’s gravitational pull (and that would be at the altitude where the escape velocity is 1 km/s). However, it’s not practical to do it that way and that is because the rocket will have to burn fuel for the entire time which, in its turn, means it will be supporting the useless weight of the fuel and not the payload. It’s more efficient to burn off that fuel much faster and accelerate to a higher speed to avoid wasting energy supporting all that weight. There are other tricks, such as using multi-stage rockets to avoid carrying too much “dead weight” into orbit.

Why do we have to launch a satellite with escape velocity?

First of all, only inter-planetary missions are given the escape velocity. I will try to answer this as simple I can.Now, look at the above picture. Imagine you've climbed a tower or a tall building. Try to throw a ball horizontally. It will hit the ground at some point. Next, you try to throw the ball with more effort. You'll notice that it has hit the ground further away from the first point. If you try to increase the velocity continuously in subsequent attempts, eventually you will see that the ball has completed one circle and it never touches the ground. The speed at which this phenomenon has occurred is the orbital velocity at that altitude. As you go high, i.e away from the surface, one will notice that the velocity to orbit will drop inversely proportional to the square root of the distance from the center of the Earth. This the principle with which rockets are launched. Scientists calculate what is the optimum height to keep the satellite in the orbit considering many constraints.              Now regarding the escape velocity, it is the minimum velocity with which an object has to be thrown so that it escapes the clutches of Earth's gravity. If you look at the above picture, the path shown by 'E' is the path taken by the object, if you throw it with an escape velocity. If you throw with velocity more than the orbital velocity at that altitude, you'll notice the object to form an ellipse about the earth. In this picture it is shown by the path 'D'. As you increase velocity, you'll notice that the ellipse is getting bigger. Eventually, there will be a velocity at which the object never returns back. This is called the escape velocity at that altitude. Suppose if your satellite is intended to go to Mars or Jupiter, then only you'll impart escape velocity. For normal satellites, escape velocity is not given. We want these satellites to continuously orbit the Earth.           One more thing, if you see the above picture, paths 'C' and 'D' are ellipses about the earth whereas path 'E' is a parabola. If the satellite takes greater velocity than the escape velocity, path taken by the satellite is a hyperbola.       ONCE AGAIN I WOULD LIKE TO REMIND YOU THAT ONLY IN INTER-PLANETARY MISSIONS, ESCAPE VELOCITY IS IMPARTED.