U3AOS2 Topic 1: Gravitational Fields

The Gravitational Field Strength of an object is changed by both the mass of the attracting object and the radius between the centres of the object being attracted and the attracting object. It's modelled with the relation:

\[ g = G\frac{M}{r^2} \]

where $ G = 6.67 \times 10^{-11} \frac{N m^2}{s^2} $ and represents the Universal Gravitational Constant

A curveball often seen is to include the altitude in the question while neglecting the radius between the centres of objects. Make sure to account and look out for this by calculating the actual radius instead of falsely using the altitude in the equation as the distance:

\[ Altitude = r − r_{planet}​ \]

There is one graph that is used and it is the Gravitational Field Strength vs Distance graph, which graphs the field strength for a range of distances for a given object.

Since the y axis is the gravitational field strength, which is g, and the x-axis is the distance between, which is h. The formula for calculating GPE, $ GPE = mgh $ can be applied here with the graph. The area under the graph represents $ gh $, which can be calculated by approximately counting the number of squares covered by the graph and the value of each square:

\[ Area under graph = (number of squares covered under the graph) \times (the value of each square) \]

To find the GPE from the graph then, the formula is to multiply the area under the graph by the mass:

\[ \Delta GPE = (area under graph) \times mass \]