Physics

Problem

1. a** The radius of the Moon's orbit about the Earth is

3.8 \times 10^8

m. Its orbital period is 27.3 days. Show that the mass of the Earth is about

6 \times 10^{24}

kg. 2. b** The gravitational field strength at the surface of Mars is 0.38 of that of the Earth. The radius of Mars is 3400 km. Calculate the mass of Mars.

Intuitive explanation

PROBLEM 1

Orbital motion is governed by gravity providing the centripetal force needed to keep the Moon in its circular path. By equating gravitational force to centripetal force and using the Moon's orbital radius and period, you can solve directly for Earth's mass—no need to know the Moon's mass.

PROBLEM 2

Gravitational field strength at a planet's surface depends on both its mass and radius. Since you know Mars's field strength relative to Earth's and Mars's radius, you can find its mass by rearranging the relationship

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

and comparing to Earth's known values.

Intuitive explanation

PROBLEM 1

PROBLEM 2

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

and comparing to Earth's known values.

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