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

Maybe c? sorry if im wrong