Gravitational Potential and Escape Speed
Gravitational potential is the work per kilogram needed to bring a mass in from infinity, which makes it negative everywhere near a source. Escape speed is the speed whose kinetic energy exactly fills that well.
What a learner can do afterwards
- Calculates potential as minus GM over r and potential energy as minus GMm over r at a stated position
- Explains the negative sign by naming infinity as the zero of the scale
- Gets escape speed by setting kinetic energy equal to the depth of the well
1 · Read
Gravitational potential is the work per kilogram needed to bring a mass in from infinity. Infinity is set as zero, so the value is negative everywhere near the source.
Lifting a 9000 kg craft from Earth's surface to 400 km up needs positive work against gravity. The gain is about 3.32 times 10 to the 10 joules, roughly ten months of one home's energy use.
Potential energy is potential times the small mass: U equals minus G M m over r. Escape speed comes from setting kinetic energy equal to the depth of the well, giving v equals root 2 G M over R. From Earth it is about 11.2 km/s ignoring air.
Negative total energy means bound and orbiting, while zero or more means escaping. Falling inward drops to lower, more negative energy, and separating needs positive work.
Potential is negative work per kilogram from infinity, and escape speed just fills that well.
2 · Watch
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Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.