Question

An exoplanet with one half of Earth's mass and 50% of Earth's radius is discovered.

What would a space cadet who weighs 800 N on Earth weigh on the exoplanet?

Answer 1

The space cadet that weighs 800 N on Earth will weigh 1,600 N on the exoplanet

Step-by-step explanation:

The given parameters are;

The mass of the exoplanet = 1/2×The mass of the Earth, M = 1/2 × M

The radius of the exoplanet = 50% of the radius of the Earth = 1/2 × The Earth's radius, R = 50/100 × R = 1/2 × R

The weight of the cadet on Earth = 800 N

`The \ weight, W =G(M * m)/(R^(2)) = 800 \ N`

Therefore, for the weight of the cadet on the exoplanet, W₁, we have;

`W_1 =G((M)/(2) * m)/( \left ( (R)/(2) \right ) ^(2)) = G((M)/(2) * m * 4)/( R ^(2)) = 2 * G * (M * m)/(R^(2)) = 2 * 800 \, N = 1,600 \, N`

The weight of a space cadet on the exoplanet, that weighs 800 N on Earth = 1,600 N.