Gravitational Potential Energy (Orbital)

Understanding Gravitational Potential Energy (Orbital)

Gravitational PE between two masses is always negative (bound system). It approaches zero as the distance increases to infinity.

How to use this calculator

1. Enter the two masses, such as a planet and a satellite.
2. Enter the distance between their centers in meters.
3. Check that the units are in kilograms and meters so the result is in joules.
4. Click calculate to find the gravitational potential energy using the formula \(U = -\frac{GMm}{r}\).

The formula explained

The formula \(U = -\frac{GMm}{r}\) computes the gravitational potential energy between two masses separated by distance \(r\). The negative sign means the energy is lower when the masses are closer together.

• U = gravitational potential energy, in joules
• G = gravitational constant, about \(6.674 \times 10^{-11}\) \(\text{N} \cdot \text{m}^2/\text{kg}^2\)
• M = first mass, in kilograms
• m = second mass, in kilograms
• r = distance between the centers of the two masses, in meters

Step by step method

1. Write down the values of \(G\), \(M\), \(m\), and \(r\).
2. Multiply \(G\), \(M\), and \(m\).
3. Divide the result by \(r\), then apply the negative sign to get \(U\).

Worked example

Problem. Find the gravitational potential energy between Earth, with mass \(5.97 \times 10^{24}\) kg, and a \(1000\) kg satellite that is \(7.00 \times 10^{6}\) m from Earth's center.

1. Use \(U = -\frac{GMm}{r}\).
2. Substitute the values, \(U = -\frac{(6.674 \times 10^{-11})(5.97 \times 10^{24})(1000)}{7.00 \times 10^{6}}\).
3. Compute the result, \(U \approx -5.70 \times 10^{10}\) J.

Tips and common mistakes

• Make sure \(r\) is the distance between the centers of the two masses, not the height above the surface.
• Keep masses in kilograms and distance in meters, because unit mistakes can change the answer a lot.

Frequently asked questions