Physics
IrvingDelio340
4

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.

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Llama11

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

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