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.

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