Question

Your spaceship lands on a moon of a small planet that orbits a distant star. As you initially circled the moon, you measured its diameter to be 5480 km. After land you observe that a simple pendulum that had a frequency of 3.50 Hz on Earth now has a frequency of 1.82 Hz. What is the mass of the moon

Answer 1

Answer:

$m=3*10^2^3kg$

Explanation:

From the question we are told that:

Moon diameter $D_m=5480Km \approx 2740000m$

Earth's frequency $F_e=3.50Hz$

Planet's frequency $F_p=1.80Hz$

 

Generally the equation for Frequency and Gravity relationship is mathematically given by

$\frac{F_p}{F_e}=\sqrt{ \frac{g_p}{g_e} }$

Therefore  gravity of Moon  is given as

$g_p= g_e*(\frac{f_p}{f_e} )^2$

$g_p= 9.8*(\frac{1.82}{3.50} )^2$

$g_p=2.64992m/s^2$

Generally the equation for mass of spherical body is mathematically given by

$m=\frac{g_pD_m^2}{G}$

where G= gravitational constant

$m=\frac{2.64992m/s^2*(2740000m)^2}{6.67*10^{-11}}$

$m=2.98268956*10^2^3kg$

$m=3*10^2^3kg$