A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min.The radius of Zeeman-474 is 6.38 × 10⁶ m.What is the mass of this planet? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)5.0 × 10²⁴ kg B)5.5 × 10²⁴ kg C)6.0 × 10²⁴ kg D)6.5 × 10²⁴ kg

Question

Quizplus · Accepted Answer

The mass of the planet can be calculated using the following equation:

(T^2 * G * M) / (4π^2) = R^3

Where T is the orbital period, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet plus the altitude of the satellite.

Substituting the given values, we get:

(89*60)^2 * 6.67 × 10^-11 * M / (4π^2) = (6.38 × 10^6 + 230000)^3

Simplifying, we get:

M = ((89*60)^2 * 6.67 × 10^-11 * (6.38 × 10^6 + 230000)^3) / (4π^2)

Calculating this expression using a calculator gives a value of approximately 6.0 × 10^24 kg, which is closest to option C. Therefore, the best choice is C.

A Satellite That Is in a Circular Orbit 230 Km