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

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

Step-by-step 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

`(F_p)/(F_e)=\sqrt{ (g_p)/(g_e) }`

Therefore gravity of Moon is given as

`g_p= g_e*((f_p)/(f_e) )^2`

`g_p= 9.8*((1.82)/(3.50) )^2`

`g_p=2.64992m/s^2`

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

`m=(g_pD_m^2)/(G)`

where G= gravitational constant

`m=(2.64992m/s^2*(2740000m)^2)/(6.67*10^(-11))`

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

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