Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

On Mars, the gravitational field strength is about $\frac{1}{4}$ of that on Earth. The mass of Earth is approximately ten times that of Mars.

What is $\frac{\text{radius of Earth}}{\text{radius of Mars}}$ ?

A. 0.4

B. 0.6 

C. 1.6 

D. 2.5

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

The centre of the Earth is separated from the centre of the Moon by a distance D. Point P lies on a line joining the centre of the Earth and the centre of the Moon, a distance X from the centre of the Earth. The gravitational field strength at P is zero.

What is the ratio $\frac{\text{mass of the Moon}}{\text{mass of the Earth}}$?

A.  $\frac{{\left(D-X\right)}^2}{X^2}$

B.  $\frac{\left(D-X\right)}{X}$

C.  $\frac{X^2}{{\left(D-X\right)}^2}$

D.  $\frac{X}{D-X}$

(i) Define gravitational field strength.

(ii) State the SI unit for gravitational field strength.

Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

Determine the gravitational field of the planet.

The following data are given:

Mass of planet            $=8.0\times {10}^{24}$ kg
Radius of the planet    $=9.1\times {10}^6$ m.

The gravitational field strength at the surface of Earth is g. Another planet has double the radius of Earth and the same density as Earth. What is the gravitational field strength at the surface of this planet?

A.  $\frac{g}{2}$

B.  $\frac{g}{4}$

C.  2g

D.  4g

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F