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Wittaler [7]
3 years ago
12

(Please help ASAP) A new planet MPSM, Mystery Planet of Spartan Men, is discovered following the orbital path of the Mystery Pla

net 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?
Physics
1 answer:
Montano1993 [528]3 years ago
8 0

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

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