Escape Velocity

Earth and the Planetary systems are not as simple as they seem. They are complex combinations of physics staying together under the effect of the gravitational field. In your physics classes, you would have read that the Earth’s Gravitational pull is 9.8 m/s which is the effect of the Earth’s mass. This means that when you leave a body to freefall under the influence of the gravity for the 1st second its velocity is 9.8 m/s and in the next second the velocity is 19.6 m/s. Earth’s gravity accelerates the body at 9.8m/s. But for an object to leave the Earth’s gravitational influence it must have a velocity called as the escape velocity. Let’s chuck the formula and the derivation and go into the value. The Earth’s escape velocity is 11.2 km/s. Knowing that this is the escape velocity, now try to guess the velocity of the satellites in the orbit? Have they left the Earth’s gravitational field yet? No. So they are flying around the Earth at higher velocity but still less than the escape velocity. Let’s consider the International Space Station. It's flying around 400 Kms from the surface of the Earth. The orbital velocity of ISS is around 7.67 Km/s. The escape velocity of the Earth is given by the formula Srqt(2GM/r) where G is the Universal Gravitational Constant, M is the Mass of the Earth and R is the radius of the Earth. The Mean radius of the Earth is 6371 Km.

So now if we decide to leave for Mars, that’s when we must provide the escape velocity to the satellite in the orbit. Almost no launchers that we have now provide the required escape velocity directly within the Earth’s atmosphere. This is due to the complexity and due to the efficiency issues. The satellite is placed in the orbit with enough fuel to obtain the escape velocity in the successive manoeuvres. Let’s consider a satellite at Low Earth Orbit. If you have seen Mangalyaan movie, then you would know the successive burns that were done to place the satellite in the elliptical orbits. When the satellite reaches the necessary velocity, the final burn is given to reach the escape velocity and to leave the Earth’s Sphere of Influence towards Mars. The velocity given must be a little higher than the escape velocity to leave the Earth Sphere of influence. It attains a hyperbolic velocity as shown in the figure., which is explained by conics (Will be explained another time). But what if you give exactly the required amount of escape velocity? It attains a path of parabolic trajectory. And less than the escape velocity? It will remain in the elliptic or circular trajectory around Earth. Now an interesting question to find out for yourself. The escape velocity of our sun is 615 Km/s. So, all the planets, asteroid and comets revolving around the sun at such enormous distance must be within the escape velocity, right? Check it out yourself.