Question

.A low Earth orbit (LEO) is an orbit around Earth with an altitude between 160 kilometers (99 mi) (orbital period of about 88 minutes). If the radius of the earth is around 6400km, what is the speed of a satellite (in Km/s) on this LEO?

Answer 1

The speed of a satellite on this LEO which will be given by -

v = G m_E / r

where, G = graviatational constant = 6.67 x 10^-11 N.m²/kg²

m_E = mass of the Earth = 5.972 x 10²⁴ kg

r = radius from the center of Earth = r_E + h

then, we get

v = [(6.67 x 10^-11 N.m²/kg²) (5.972 x 10²⁴ kg)] / [(6.4 x 10⁶ m) + (1.6 x 10⁵ m)]

v = [(3.983 x 10¹⁴ N.m²/kg) / (6.56 x 10⁶ m)]

v = 6.0716 x 10⁷ m/s

v = 7792.05 m/s

Converting m/s into km/s :

v = 7.792 km/s