Student Projects

Independent-learning super-curriculum projects: reading, research and ideas shared by Perse students

Gravitational Field Strength of a Planet – Does it Matter Where You Are in Relation to the Planet?

Aaditya N, Year 7

The gravitational field strength depends on mass and size (radius) of the planet. The direction of change (increasing or decreasing) is given by the inverse square law. Inverse square law applies to point sources. Though planet in general is not point object, the centre of mass model treats as point mass. Gravitational field strength at a point is defined as the force per unit mass exerted on a mass placed at that point. (g= – GM/r2. This can be obtained by combining the two definitions of force, F =mg    and F = -GMm/r2; the minus sign is just the representation that the force is attractive. G is the universal gravitational constant, but the masses M (mass of the planet), m (the mass under the planet’s influence) and the distance “r” between them are variables).

Local variations in planet’s topography (e.g. mountains) may also influence planet gravitational field (though minimal). The kind of matter (denser ore minerals, or less dense sedimentary rocks) also influences.

Sun has around 28 times more gravity than that of earth. But its radius is 100 times than that of earth, meaning the volume of sun is million times of earth. When we substitute these values into inverse square law, the expected gravitational field increase of sun is around 100 times than that of earth. But the observed solar gravity is around four times less than expected. This is due to the lower density of solar matter.

By taking the volume formula of a sphere, and using the definition of density as the quantity of matter contained in a unit volume, we can write gravitational field as a function of density and can show that, for a fixed volume, it is directly proportional to density.

There is an interesting graph (  :Astronomy Section ) that shows a linear relationship between gravitational field and mass/squared distance with an appropriate scaling factor.

Grav-Planet Graph

In addition to the size, the shape also matters. Because of the rotation of celestial objects, there will be uneven distribution of matter. This results in oblate profile, instead of having an ideal spherical shape. This changes the objects distribution of matter.

Density is very important factor as it is very prominent in objects like neutron stars and white dwarf.

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