Answer:
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.
