Question

A robot probe lands on a new, uncharted planet. It has determined the diameter of the planet to be 8 × 106 m. It weighs a standard 1 kg mass and determines that 1 kg weighs only 5 newtons on this new planet.

(a) What must the mass of the planet be?

(b) What is the acceleration due to gravity on this planet?

Answer 1

Answer on Question #83667, Physics / Astronomy | Astrophysics

Question:

A robot probe lands on a new, uncharted planet. It has determined the diameter of the planet to be 8 × 106 m. It weighs a standard 1 kg mass and determines that 1 kg weighs only 5 newtons on this new planet.

(a) What must the mass of the planet be?

(b) What is the acceleration due to gravity on this planet?

Solution:

If the weight of 1 kg mass W = 5 N, than this planet g is equal to 5 m/s², as far as W = mg. According to the law of gravity $mg = \frac{GmM}{R^2}$, what means $M = \frac{R^2g}{G} = \frac{64\cdot 10^{12}\cdot 5}{4\cdot 6.67\cdot 10^{-11}} = 1.2\cdot 10^{24}$ (kg).

The answer:

a) the mass of the planet equals to $1.2 \cdot 10^{24} \, \mathrm{kg}$;

b) the acceleration due to gravity equals to $5 \, \mathrm{m/s}^2$.

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