Science Articles

WHAT ARE THE DEPENDENCIES OF ESCAPE VELOCITY?

We all are aware that gravity attracts the object towards Earth. If we throw the ball upwards, eventually it returns back to Earth. But we all know that artificial satellites are sent from the surface of earth towards the space. Are they not pushed by gravity towards the Earth? How do they reach the space? Here is where escape velocity comes in.


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INTRODUCTION

We all are aware that gravity attracts the object towards Earth. If we throw the ball upwards, eventually it returns back to Earth. But we all know that artificial satellites are sent from the surface of earth towards the space. Are they not pushed by gravity towards the Earth? How do they reach the space? Here is where escape velocity comes in.

DEFINITION

Escape velocity is the lowest velocity that an object needs to negate the gravitational force. That is to say the velocity should be enough that the object escapes the gravity and moves out before gravity can pull it down. For example, a spacecraft needs to have a velocity of 25000 miles per hour to escape gravity and enter the space where gravity no longer exists.

MATHEMATICAL FORMULA

Escape velocity can be calculated as –

V = (2 * G * M / r) ½

where V is the escape velocity, G is the gravitational constant, M is the mass of the body, and r is the radius is the distance between two bodies.

For example, Earth has a mass of 5.98 x 1024 kg, radius of 6.37 x 106 meters, and G = 6.67*10-11 N-m2 /Kg2. What will be the escape velocity of Earth?

V = (2 * 6.67*10-11 * 5.98 x 1024  / 6.37 x 106 ) ½

V = 1.12 * 104 meters per second.

Therefore, the escape velocity of Earth is 1.12 * 104 meters per second.

DEPENDENCY ON MASS

Escape velocity is directly proportional to the mass of the body. A satellite leaving from Moon’s surface needs a lower escape velocity to move out of Moon’s gravity. A satellite leaving from Earth’s surface needs a higher escape velocity to move out of Earth’s gravity. This is because gravity of Moon is less than the gravity of Earth. Similarly, a satellite leaving from Jupiter’s surface needs a too much higher escape velocity to move out of Jupiter’s gravity, because Jupiter has a higher mass and higher gravity than Earth.

IMPORTANCE OF RADIUS

Which is better, to launch a satellite in space from near the equator or far away from the equator? Since, escape velocity is inversely proportional to the radius, larger radiuses are preferred. At near the equator, radius is greater, so escape velocity is less. At poles, radius is less so escape velocity is more. Therefore, space centers are situated near the equator.