Minimum Energy Required to launch a satellite
Minimum Energy Required to launch a satellite of mass m from the surface of the earth is the sum of gravitational potential energy and kinetic energy needed for the satellite to achieve the desired orbit.
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m: Mass of the satellite
G: Gravitational constant, 6.67408 × 10-11 m3 Kg-1 s
R: Radius of the earth
r: Distance from the planet's center to the satellite in orbit
The circular orbit at an altitude of from the center is 2R
Gravitational constant: The gravitational constant (G) is a physical constant represented by the symbol G and is used to calculate the gravitational force between two objects.
Radius of Earth: According to NASA the polar radius is 6356.752 Km, the Equatorial radius is 6378.137 Km, and the Volumetric mean radius is 6371 Km
Kinetic energy (KE) = 1/2 mv2
Gravitational potential energy (PE) = -GMm/r
Minimum energy required, Emin = 1/2 mv2 - GMm/r = 5 GMm/6R
For example: if m=500 Kg, M is 5.9722×1024 Kg, G is 6.67408 × 10-20 Km3 Kg-1 s (given in Km) and R is 6371 Km
Then,
Emin = 5 GMm/6R = 2.60679515094438E+44