# Gravitational attraction and the planets

If you were to make a journey across our Solar System and land on different planets you would notice that you weighed different amounts on the different planets. This is because the gravitational field on their surface is different one from the other.

If the gravitational field was double that on Earth you would weigh twice as much as you do on Earth – and so would everything else!

 Planet Mass(Earth = 1000) Radius(km) Density(kg/m3 Gravitational field (N/kg) Mass/Radius2 (N/kg) Mercury 55 2440 5420 3.8 9.2 Venus 812 6050 5250 8.8 22.2 Earth 1000 6400 5510 9.8 24.4 Mars 110 3380 3960 3.8 9.6 Jupiter 317000 71400 1330 25 62.2 Saturn 95000 60400 680 10.4 26.0 Uranus 14500 23600 1600 10.4 26.0 Neptune 16700 22300 1650 13.8 33.6

You should be able to see from the table that this gravitational field at the surface of a planet does not just depend on the mass of the planet. For example, if you look at the gravitational field at the surface of Saturn it is the same as that on the surface of Uranus although Saturn is much more massive.

The size of this gravitational field is very important – if it too large we would be pulled so strongly to the surface that we would be crushed. For this reason creatures that lived on planets with high gravitational fields (high g) would need strong skeletons and really thick legs!

The graph shows the way in which mass and radius affect the size of the gravitational field.

The following graph gives you a way of working out the gravitational field on any planet, or other astronomical body such as one of the moons in the solar system, if you know its mass and its radius.

Pluto (a minor planet orbiting the Sun usually outside the orbit of Neptune) has a mass of 2.1 (compared with the Earth at 1000) and a mean radius of 1195 km. From a detailed version of the graph the graph the value of g on the surface of Pluto would be 0.58 N/kg.

Another way of finding the value of g is to use the radius of the planet and its density.

Use the data four the first four planets in the table to plot a graph of the surface gravitational field (g) against the (density x radius)/1000000.

Use your graph to work out the surface gravitational field on the following moons of the Solar System.

 Moon Radius (km) Density(kg/m3 Io (a moon of Jupiter) 1830 3550 Ganymede (a moon of Jupiter) 2634 1940 Callisto (a moon of Jupiter) 2403 1860 Titan (a moon of Saturn) 2576 1880 Titania (a moon of Uranus) 789 1600 Triton (a moon of Neptune) 1352 2070

(Photograph: courtesy of NASA)

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© Keith Gibbs 2020