Expert reviewed • 04 March 2025 • 8 minute read
Gravitational potential energy is a fundamental concept in physics that describes the energy an object possesses due to its position within a gravitational field. This concept is crucial for understanding the behaviour of objects in space, planetary motion, and satellite orbits.
In a radial gravitational field, such as those surrounding planets and stars, the gravitational potential energy of an object is given by:
Where:
Aspect | Near Earth Surface | In Space |
---|---|---|
Formula | ||
Assumption | Constant gravitational field | Variable gravitational field |
Application | Small displacements near Earth's surface | Large distances in space |
For objects in orbit, the total energy is the sum of kinetic energy and potential energy :
This equation shows that the total energy of an orbiting body is negative and equal to half its potential energy.
Calculate the total energy of a 1000 kg satellite orbiting Earth at an altitude of 200 km. (Earth's mass , Earth's radius = 6371 km)
Calculate orbital radius:
Apply the total energy formula:
The negative value indicates that the satellite is bound to Earth's orbit.
When a satellite moves between orbits, its total energy changes. The work done to change orbits is equal to the change in total energy:
Where,
A 500 kg satellite is moved from a circular orbit at an altitude of 300 km to a new circular orbit at 800 km. Calculate the energy change and work done.
Initial radius:
Final radius:
Calculate energy change:
The positive value indicates an increase in energy, which makes sense as the satellite is moved to a higher orbit.
Work done in a gravitational field is directly related to changes in gravitational potential energy: