Question

An astronaut orbits planet Y in her spaceship. To remain in orbit at 410km above the planet's center, she maintains a speed of 68 m/s. What is the mass of planet Y? Note: the constant of universal gravity (G) equals 6.674 × 10-11 N ⋅ m2/kg2.

Answer 1

Formula for orbital speed, v =  √(GM/R)

Where G is the universal gravitational constant, M = Central Mass,

R = Distance between centers of Mass.

Given.  v = 68 m/s, M = ? , R = 410 km = 410000 m., G = 6.674 * 10⁻¹¹ Nm²/kg²

68 = √(GM/R)

68 = √(6.674 * 10⁻¹¹ * M/410000)

68² =  (6.674 * 10⁻¹¹ * M)/410000

(68²  * 410000) / 6.674 * 10⁻¹¹    = M

2.84 × 10¹⁹    = M

Mass of Planet Y =  2.84 × 10¹⁹ kg