The planet Mars has a mass of$6.4\times {10}^{23}\mathrm{kg}$and a diameter of $6790 \mathrm{km}$. Calculate the acceleration due to gravity at the planet's surface.

 

The planet Mars has a mass of$6.4\times {10}^{23}\mathrm{kg}$and a diameter of $6790 \mathrm{km}$. Calculate the gravitational potential at the surface of the planet.

The planet Mars has a mass of$6.4\times {10}^{23}\mathrm{kg}$and a diameter of $6790 \mathrm{km}$. A rocket is to return some samples of Martian material to Earth. Write down how much energy each kilogram of matter must be given to escape completely from Mars' gravitational field.

The planet Mars has a mass of$6.4\times {10}^{23}\mathrm{kg}$and a diameter of $6790 \mathrm{km}$.if gravitational potential energy is$1.26\times {10}^7 J$ then show that the minimum speed that the rocket must reach to escape from the gravitational field is $5000\mathrm{m} {\mathrm{s}}^{-1}$.

The planet Mars has a mass of$6.4\times {10}^{23}\mathrm{kg}$and a diameter of $6790 \mathrm{km}$. Suggest why it has been proposed that, for a successful mission to Mars, the craft that takes the astronauts to Mars will be assembled at a space station in Earth orbit and launched from there, rather than from the Earth's surface.

This diagram shows the gravitational potential near a planet of mass M and radius R.

On a copy of the diagram, draw similar curves. For a planet of the same radius but of mass $\mathit{2}M\mathit{-}$label 
this i. 

This diagram shows the gravitational potential near a planet of mass M and radius R.

On a copy of the diagram, draw similar curves. For a planet of the same radius but of radius $\mathit{2}R\mathit{-}$label this ii.