As we know, the moon is a satellite of our earth, what is the
theoretical period of the moon? The average radius of the
moon's orbit is 3.84 108 m and the mass of the earth is 5.97 x
1024 kg (in hours, G = 6.67 x 10-9 N (m/kg) 3).

Answer:c

Explanation:c

This question involves the concepts of the time period, orbital radius, and gravitational constant.

The theoretical period of the moon is "658 hr".

The theoretical time period of the moon around the earth can be found using the following formula:

[tex]\frac{T^2}{R^3}=\frac{4\pi^2}{GM}[/tex]

where,

T = Time Period of Moon = ?

R = Orbital Radius = 3.84 x 10⁸ m

G = Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

M = Mass of Earth = 5.97 x 10²⁴ kg

Therefore,

[tex]\frac{T^2}{(3.84\ x\ 10^8\ m)^3}=\frac{4\pi^2}{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(5.97\ x\ 10^{24}\ kg)}\\\\T^2=(9.91\ x\ 10^{-14}\ s^2/m^3)(56.62\ x\ 10^{24}\ m^3)\\\\T=\sqrt{561.34\ x\ 10^{10}\ s^2}[/tex]

T = 2.37 x 10⁶ s[tex](\frac{1\ h}{3600\ s})[/tex]

T = 658 hr

Learn more about the orbital time period here:

https://brainly.com/question/14494804?referrer=searchResults

The attached picture shows the derivation of the formula for orbital speed.

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