Question

For a satellite at a height of 25,000 miles, at what speed must the satellite be traveling to achieve a circular orbit? (A score of 100% will tell you that you have achieved a circular orbit).

Answer 1

using an equation,

V = G M / r                                 { eq. 1 }

where, G = universal gravitational constant = 6.67 x 10^-11 Nm²/kg²

M = mass of the earth = 5.97 x 10²⁴ kg

r = distance of satellite from earth center = R + h                       { eq. 2 }

R = radius of the earth = 6.37 x 10⁶ m

h = height of satellite from the earth surface = 25000 miles = 4.02 x 10⁷ m = 0.4 x 10⁶ m

inserting the value of 'R' & 'h' in eq.2

r = (6.37 x 10⁶ m) + (0.4 x 10⁶ m)

r = 6.77 x 10⁶ m

now, inserting all these values in eq.1

V = (6.67 x 10^-11 Nm²/kg²) (5.97 x 10²⁴ kg) / (6.77 x 10⁶ m)

V = (39.81 x 10¹³) / (6.77 x 10⁶ m)

V = 5.88 x 10⁷ m/s

V = 7668.1 m/s