Question

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?
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

Answer: The correct answer is Earth's orbital period and distance from the Sun.

Explanation: Rosalinda can use Kepler's Laws to determine the mass of the Earth. Third law of Kepler is the most convenient for this purpose.

Expression for Kepler's Third Law is:

$P^2=\frac{4\pi ^2}{k^2(M_{sun}+M_{earth})}a^3$

Where,

P =  orbital period determined in days

k = Gaussian Gravitational constant with value 0.01720209895

$M_{sun}$ = Mass of the sun which is known to us which is $1.989\times 10^{30}kg$

$M_{Earth}$ = Mass of Earth which has to be determined

a = Semi major axis which is the distance of Earth from the sun.

Hence, Earth's orbital period and its distance from the sun is useful in determining the mass of Earth.

Answer 2

The best and most correct answer among the choices provided by the question is the second choice "the moon’s orbital period and distance from Earth" 


 The Earth's mass is 5.9736 x 1024 kg. That's a big number, so let's write it out in full: 5,973,600,000,000,000,000,000,000 kg. You could also say the Earth's mass is 5.9sextillion tonnes. Phew, that's a lot of mass.

I hope my answer has come to your help. God bless and have a nice day ahead!