Ganymede is the largest of Jupiter's moons, with a mass of $1.48\times {10}^{23}\mathrm{kg}$. It orbits Jupiter with an orbital radius of $1.07\times {10}^6\mathrm{km}$ and it rotates on its own axis with a period of $7.15$ days. It has been suggested that to monitor an unmanned landing craft on the surface of Ganymede a geostationary satellite should be placed in orbit around Ganymede. Calculate the orbital radius of the proposed geostationary satellite.  

The Earth orbits the Sun with a period of $1$ year at an orbital radius of $1.50\times {10}^{11} \mathrm{m}.$ Calculate:

(a). The orbital speed of the Earth

The Earth orbits the Sun with a period of $1$ year at an orbital radius of $1.50\times {10}^{11} \mathrm{m}.$ Calculate the centripetal acceleration of the Earth.

The Earth orbits the Sun with a period of $1$ year at an orbital radius of $1.50\times {10}^{11} \mathrm{m}.$ Calculate the Sun's gravitational field strength at the Earth

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.