The weight of spaceman Speff at the surface of planet X, solely due to its gravitational pull, is 389 N. If he moves to a distance of 1.86 * 104 km above the planet's surface, his weight changes to 24.31 N. What is the mass of planet X, if Speff's mass is 75.0 kg? (G = 6.67 * 10 - 11 N ∙ m2/kg2)

mass of the planet X = 5.6 * 10²³ kg.

Explanation:

According to Newtons law of universal gravitation,

F = GM₁M₂/r²

Where F = gravitational force, M₁ = mass of the speff, M₂ = mass of the planet X, G = gravitational constant r = distance between the speff and the planet X

making M₂ The subject of the equation above,

M₂ = Fr²/GM₁ ... equation 2

Where F = 24.31 N, r = 1.08*18⁴km ⇒ (convert to m) = 1.08 * 10⁴ * 1000 m

r = 1.08 * 10⁷ m, G = 6.67 * 10 ⁻¹¹ Nm²/kg², M₁ = 75 kg

Substituting this values in equation 2,

M₂ = 24.13 (1.08 * 10⁷) ²/75 (6.67 * 10 ⁻¹¹)

M₂ = 24.13 * 1.17 * 10¹⁴/500.25 * 10⁻¹¹

M₂ = (28.23 * 10¹⁴) / (500.25 * 10⁻¹¹)

M₂ = 0.056 * 10²⁵

M₂ = 5.6 * 10²³ kg.

Therefore mass of the planet X = 5.6 * 10²³ kg.