Calculate the potential energy of a spacecraft of mass $250 \mathrm{kg}$, when it is $20 000 \mathrm{km}$ from the planet Mars. (Mass of Mars $= 6.4 \mathrm{x} 1023 \mathrm{kg}$, radius of Mars $=3.4\times {10}^6\mathrm{m}.$)

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.  

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.

(b). Suggest a difficulty that might be encountered in achieving a geostationary orbit for this moon.

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.