An isolated planet is modelled as a uniform sphere.

Two identical uniform spherical asteroids each have mass $m$ and their centres are separated by a distance $r$. The gravitational force between them has magnitude $F$. The mass of one asteroid is then doubled and the separation of their centres is made $3r$.

The Moon's gravitational field acts on Earth and is involved in producing ocean tides. Earth is an extended body.

Two small moons move in circular orbits around the same planet. Moon X has orbital radius $r$ and period $T$. Moon Y has orbital radius $3r$.

The diagram shows equipotential surfaces around an isolated spherical planet.

The table and graph show data for four moons orbiting the same planet. The orbits may be assumed to be circular.

A small laboratory mass is moved along a line away from a much larger spherical mass. The graph shows the measured gravitational force on the small mass as a function of separation between the centres of the masses.

Two spherical bodies A and B have masses $M$ and $4M$ respectively. Their centres are separated by distance $d$. Point P is halfway between their centres.

A satellite of mass $800\ \text{kg}$ is moved slowly from a circular orbit of radius $7.0\times 10^6\ \text{m}$ to a circular orbit of radius $1.4\times 10^7\ \text{m}$ around a planet of mass $6.0\times 10^{24}\ \text{kg}$. The change in kinetic energy during the transfer is not considered in this question.

At two nearby points in the radial gravitational field of a moon, the gravitational potential changes from $-3.10\times 10^7\ \text{J kg}^{-1}$ to $-3.04\times 10^7\ \text{J kg}^{-1}$ when moving $2.0\times 10^5\ \text{m}$ outward from the moon.

A spacecraft of mass $1200\ \text{kg}$ is moved from the surface of a non-rotating planet to a circular orbit. The gravitational potential at the surface is $-6.25\times 10^7\ \text{J kg}^{-1}$ and the gravitational potential at the orbit is $-5.80\times 10^7\ \text{J kg}^{-1}$. In the circular orbit the spacecraft speed is $7.6\times 10^3\ \text{m s}^{-1}$.

A satellite in a low circular orbit experiences a small viscous drag force due to the upper atmosphere.

An asteroid and a planet are represented in the annotated diagram. Two possible separations of the asteroid from the planet are shown. The asteroid is irregular but its centre of mass is marked.

A probe measures the gravitational field strength at different distances from the centre of a spherical moon. The moon may be treated as a point mass outside its surface.

Four diagrams proposed by students show gravitational field lines around a single isolated spherical planet. The planet is represented by a circle in each diagram.

Two small spherical masses are brought slowly from a very large separation to different separations $r$. The graph shows the gravitational potential energy $E_p$ of the two-mass system as a function of $1/r$.

The diagram shows gravitational equipotential lines in a plane around a spherical planet. The values of gravitational potential are labelled on several lines.

A satellite is in a circular orbit of radius $1.75\times 10^6\ \text{m}$ around a small planet. For the planet, $GM=4.90\times 10^{12}\ \text{m}^3\ \text{s}^{-2}$. An engine burn is made in the direction of motion at this same radius.

Two isolated spherical bodies A and B are fixed in space. Points on the line joining their centres are labelled by the distance $x$ from the centre of A. The table gives the separate gravitational field strengths due to A and due to B at several points. A field directed to the right is taken as positive.

A spacecraft moves radially away from a spherical planet. The graph shows gravitational potential $V_g$ as a function of distance $r$ from the centre of the planet. A short tangent is drawn at point P.

A mission team calculates the circular orbital speed and escape speed at different orbital radii around a planet. The graph shows both speeds as functions of orbital radius $r$.

The graphs show data from a low-altitude satellite over several months. No engine boost was made during the interval.

A comet moves in an elliptical orbit around the Sun. The diagram shows four positions of the comet during one orbit.

Two small spherical asteroids, X and Y, are separated by a centre-to-centre distance of $8.0\times10^3\ \text{m}$. The mass of X is $6.0\times10^{12}\ \text{kg}$ and the mass of Y is $2.0\times10^{12}\ \text{kg}$.

A spherical planet has a small moon nearby. The planet has a much greater mass than the moon.

A spacecraft passes through the gravitational field of an isolated spherical moon. A map of equipotential surfaces near the moon is shown.

A satellite of mass $850\ \text{kg}$ is to be placed into a circular orbit around a non-rotating planet. The table gives properties of the planet and the target orbit.

A small probe is placed on the line joining the centres of a planet P and its moon M. The mass of P is $6.4\times10^{23}\ \text{kg}$, the mass of M is $8.0\times10^{21}\ \text{kg}$ and the centre-to-centre separation is $4.0\times10^8\ \text{m}$. Point X is $1.0\times10^8\ \text{m}$ from the centre of P.

A lander descends towards a spherical planet of radius $3.2\times10^6\ \text{m}$. The gravitational field strength at the surface is $4.0\ \text{N kg}^{-1}$. The planet may be assumed to have uniform density.

An exoplanet is observed to move in an approximately circular orbit around a star. The orbital radius is $7.5\times10^{10}\ \text{m}$ and the orbital period is $1.1\times10^7\ \text{s}$.

Two identical spherical asteroids, each of mass $3.0\times10^{14}\ \text{kg}$, are initially very far apart and at rest. They are then brought to a centre-to-centre separation of $2.0\times10^5\ \text{m}$.

A graph shows the gravitational potential $V_g$ around a spherical planet as a function of distance $r$ from its centre.

A satellite of mass $600\ \text{kg}$ moves from a circular orbit of radius $7.0\times10^6\ \text{m}$ to a higher circular orbit of radius $1.4\times10^7\ \text{m}$ around Earth. Take the mass of Earth to be $6.0\times10^{24}\ \text{kg}$.

A $950\ \text{kg}$ spacecraft is in a circular parking orbit around a planet of mass $5.0\times10^{24}\ \text{kg}$. The orbital radius is $8.0\times10^6\ \text{m}$.

A low-orbit satellite experiences a small viscous drag force due to the upper atmosphere. Over many orbits the satellite moves from an orbit of radius $6.9\times10^6\ \text{m}$ to an orbit of radius $6.7\times10^6\ \text{m}$ around Earth.