Question

Suppose that a spacecraft goes into orbit about an unknown moon. Suppose that the altitude (above the surface) at periapsis is 1000 km (kilometers) and at apoapsis the altitude (above the surface) is 5000 km. Suppose that the radius of the moon is approximately 1000 km. The period of the vehicle’s orbit about the moon is 9.5 hours. Estimate the mass of this moon. The universal gravitational constant is G

Answer 1

Answer:

M = 1.3667 × 10²² Kg

Explanation:

given,

altitude above at periapsis = 1000 Km

altitude at apoapsis = 5000 Km

radius of moon = 1000 Km

periodic vehicle orbit about moon is = 9.5 hours

mass of the moon = ?

time period = 9.5 hours

G = 6.68 x 10⁻²⁰ Km³/sec².Kg

using keplers formula

$T^2 = \dfrac{4\pi^2}{GM}a^3$

where a is semi major axis

$a = \dfrac{5000+1000}{2}$

a = 3000 Km

$M = \dfrac{4\pi^2}{GT^2}a^3$

$M = \dfrac{4\pi^2}{6.68 \times 10^{-20}\times (9.5\times 60\times 60)^2}3000^3$

M = 1.3667 × 10²² Kg