Question

(Please help ASAP) A new planet MPSM, Mystery Planet of Spartan Men, is discovered following the orbital path of the Mystery Planet of Amazon Women. The gravitational field of the MPSM is measured during a satellite fly-by as 1.33 m/s2 at a distance of 5 planetary radii from the center of MPSM. What is the expected strength of the planet's gravity on its surface?

Answer 1

Answer:

$33.25 m/s^2$

Explanation:

The strength of the gravitational field produced by a planet at a distance r from the centre of the planet is given by

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

where

G is the gravitational constant

M is the mass of the planet

r is the distance from the centre of the planet

We can rewrite the equation as

$gr^2 = GM$

And since the term on the right is constant, we can write

$g_1 r_1^2 = g_2 r_2^2$

where $g_1,g_2$ are the strength of the gravitational field measured at two difference distances r1, r2.

In this problem we have:

$g_1 = 1.33 m/s^2$ when the distance is 5 planetary radii, so

$r_1 = 5R$

where R is the planetary radius.

Therefore, at the surface,

$r_2 =R$

And the strength of the gravitational field is

$g_2 = \frac{g_1 r_1^2}{r_2^2}=\frac{(1.33)(5R)^2}{R^2}=(1.33)(25)=33.25 m/s^2$