Newton’s concept of a satellite's orbit
•Newton created a hypothetical scenario as follows. A person climbed a very tall mountain and launched a projectile horizontally from the peak. The projectile follows a parabolic path (see the above discussion relating to projectile motion) before striking the ground. If another projectile were launched faster than the first, then it would travel further before striking the ground. If yet another projectile were launched fast enough, then it should be able to travel right around the Earth because, as it falls, the surface of the Earth curves away from it. The curve of the projectile’s motion would follow that of the earth’s surface and thus not hit it. This projectile would then be in a circular orbit at a fixed height above the earth’s surface.
•If a projectile is launched still faster, its orbit will stretch out into an elliptical shape. Even faster launch velocities result in the projectile following a parabolic or hyperbolic path away from the Earth, escaping it entirely.
Circular Velocity (Orbital Velocity)
Orbital velocity (also called circular velocity) is the speed of a satellite in orbit around a planet. The formula for circular velocity is given as:
where r = R+hTime period of Satellite
Geostationary satellite
A satellite whose period of revolution is 24 hours, is a geostationary satellite
It always appears to be at a fixed point in space, because the period of rotation of the Earth about its own axis is also equal to 24 hours.
Knowing T = 24 hours, g = 9.8 ms-1, the height of a geostationary satellite is calculated to be 36000km
Its orbital velocity is 3.1 km/s
Its plane of orbit is the equatorial plane
It revolves from west to east which is similar to the Earth's movement.
It is very useful in telecommunication.
Binding Energy
Total energy of an object within the gravitational field of the Earth is always given by the expression :
ETOTAL = EK + EP (Conservation of Energy)
At the earth's surface :
EK = 0
Therefore ETOTAL = EP = -(GMm)/R,
in this case the binding energy is equal to (GMm)/R.
For a satellite in circular orbit around the Earth:
The minimum velocity required by a satellite or a rocket or any other object to escape the Earth's Gravitational Potential Energy is called escape velocity (ve)
For Earth the value of escape velocity is 11.2 km/s