Gravitational Potential Energy in Space
U = −GMm/r is zero at infinity and negative closer in.
About this topic
Far from Earth the formula mgh no longer works, because g falls with distance. The correct expression is U = −GMm/r, defined as zero at infinite separation and negative closer in, showing the object is bound. mgh is just a good approximation near the surface, where the change in U over a short climb is about mgΔh.
The deeper the well, the more energy it takes to climb out. The negative sign means you must add energy to separate the masses; a total energy less than zero means the object is trapped in orbit, and a total of zero or more means it escapes. Orbital total energy is E = −GMm/(2r), so a bigger orbit has a higher (less negative) energy.
Worked example: lifting a 1000 kg satellite from Earth's surface to a 400 km orbit takes the potential energy from about −6.25 × 10¹⁰ J to about −5.9 × 10¹⁰ J, a gain of about 3.7 × 10⁹ J, plus the kinetic energy needed to move at orbital speed.
This idea explains why launching to orbit costs so much fuel, why gravitational slingshots can add speed to a probe, and why comets speed up as they fall toward the Sun. Do not worry that negative energy seems odd: only differences matter, and the zero point is just chosen at infinity for convenience.
Key ideas
- Negative means bound
- Escape needs total energy ≥ 0
- Reduces to mgh near Earth
Quick check
Use cases: where Gravitational Potential Energy in Space helps
- Homework: review the key idea behind Gravitational Potential Energy in Space before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Gravitational Potential Energy in Space without notes.
- Visual learning: play with the interactive lab to see how Gravitational Potential Energy in Space changes when you adjust its inputs.
- Teaching a friend: explain Gravitational Potential Energy in Space in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Gravitational Potential Energy in Space?
U = −GMm/r is zero at infinity and negative closer in.
What will I learn in Gravitational Potential Energy in Space?
Negative means bound. Escape needs total energy ≥ 0. Reduces to mgh near Earth.
Is Gravitational Potential Energy in Space part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Gravitational Potential Energy in Space lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Gravitational Potential Energy in Space?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.