State what is meant by gravitational field strength.

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.

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