Question

The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet ?

Answer 1

To solve this problem we will apply the Newtonian concept of gravitational acceleration produced by a planet. This relationship is given by:

$g = \frac{GM}{r^2}$

Where,

G = Gravitational Universal Constant

M = Mass of Earth

r = Radius

The values given are based on the constants of the earth, so they can be expressed as

$M_p = \frac{1}{100} M_e$

$r_p = \frac{1}{4} r_e$

The relationship of gravity would then be given:

$g_e = \frac{GM_e}{r_e^2}$

The relationship with the new planet, from the gravity of the earth would be given

$g_p = \frac{GM_p}{r_p^2}$

$g_p = \frac{G(1/100)M_e}{(1/4 r_e)^2}$

$g_p = \frac{GM_e 16}{100 r_e^2}$

$g_p = 0.16 \frac{GM_e}{r_e^2}$

$g_p = 0.16g_e$

The relationship with the weight of the earth would be given as:

$W_e = m*g_e = 600N$

$W_p = m*g_p = m(0.16g_p)$

$W_p = (m*g_p)(0.16)$

$W_p = 600*0.16$

$W_p = 96N$

Therefore the weigh on this planet would be 96N