Mercury, the smallest of the eight recognised planets, has a diameter of$4.88\times {10}^6\mathrm{m}$ $4.88\times {10}^6\mathrm{m}$and a mean density of $5.4\times {10}^3\mathrm{kg} {\mathrm{m}}^{-3}$. A man has a weight of 900 N on the Earth's surface. What would his weight be on the surface of Mercury?

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.