Rosalinda wants to calculate the mass of Earth using Kepler’s laws or Newton’s universal law of gravitation.Which data would allow her to find the mass of Earth?

Question

the mass of the Sun and the orbital period of the moon
the moon’s orbital period and distance from Earth
Earth’s distance from the Sun and the moon’s orbital period
Earth’s orbital period and distance from the Sun

Answer 1

To calculate the mass of Earth using Kepler's laws or Newton's universal law of gravitation, Rosalinda needs data that relates to the gravitational effects of Earth. The most relevant choice from the ones provided is:

the moon’s orbital period and distance from Earth.

By using the moon's orbital period (T) and the distance from Earth to the moon (r), Rosalinda can apply Newton's version of Kepler's third law, which relates these quantities to the mass of Earth (M) with the following formula:

\[ T^2 = \frac{4\pi^2}{G M} r^3 \]

Here, G is the gravitational constant. Rearranging this equation allows her to solve for the mass of Earth.