Earth has a mass of 5.97 x 10*kg, and a mean radius of 6.38 x 108m. What would be the orbital speed and period of a satellite in

orbit 1.44 x 109 m above Earth?

Centripetal acceleration = acceleration due to gravity

v² / r = GM / r²

Solving for velocity:

v = √ (GM / r)

Given:

G = 6.67*10⁻¹¹ m³/kg/s²

M = 5.97*10²⁴ kg

r = 6.38*10⁸ m + 1.44*10⁹ m = 2.078*10⁹ m

v = √ (6.67*10⁻¹¹ * 5.97*10²⁴ / 2.078*10⁹)

v = 438 m/s

Period is the time to travel one circumference:

T = 2πr / v

T = 2π (2.078*10⁹) / 438

T = 2.98*10⁷ s

T = 8290 hr

T = 345 days