Question

A space traveler weighs 525 N on earth. What will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth?

Answer 1

Answer:

$F_{planet} = 116.67N$

Step-by-step explanation:

Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, the law is given as:

$F_{G} = G\frac{m_{1} m_{2} }{r^{2} }$

$F_{G}$ = Gravitational force

G = Gravitational constant

$m_{1}$ = Mass of body 1

$m_{2}$ = Mass of body 2

r = distance between m1 and m2

We have two planets in this question: Earth and another planet

Gravitational force on earth is given as:

$F_{Earth} = G\frac{m_{Earth} m_{2} }{r_{Earth} ^{2} }$          ...Equation 1

For the planet, we were given that:

$r_{planet} = 3 * r_{Earth} \\m_{planet} = 2 * m_{Earth}$

$F_{planet} = G\frac{m_{planet}m_{2} }{r_{planet} ^{2} } = G\frac{2m_{Earth} m_{2} }{(3r_{Earth}) ^{2} } \\\\F_{planet} = \frac{2}{9}G\frac{m_{Earth} m_{2} }{r_{Earth} ^{2} }$ ....Equation 2

Replace $G\frac{m_{Earth} m_{2} }{r_{Earth} ^{2} } = F_{Earth}$ from equation 1 in equation 2.

So, we have

$F_{planet} = \frac{2}{9} F_{Earth} = \frac{2}{9} * 525N\\ \\F_{planet} = \frac{1050}{9} = 116.67N$

Therefore, the traveller will weigh 116.67N on this planet.