On the Moon, g = 1.62 m s−2 and the radius is 1.74 × 106 m. Find the escape velocity from the Moon's surface.
- Use vesc = √(2gR).
- 2gR = 2 × 1.62 × 1.74 × 106 = 5.64 × 106 m2 s−2.
- vesc = √(5.64 × 106) = 2.37 × 103 m s−1.
Answer: About 2.4 km s−1
Absolute potential energy, escape velocity and energy sources
Physics · Work and energy. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
The formula mgh only works close to the Earth's surface, where g is constant. For large distances we use absolute potential energy: the work done by gravity when a body is moved from its position to infinity. It is zero at infinity and negative everywhere else, because gravity is attractive and work must be done on the body to take it away.
Escape velocity is the least initial speed a body needs to leave the Earth and never return. Its starting kinetic energy must equal the size of its absolute potential energy at the surface. The mass of the body cancels out.
The chapter also covers non-conventional energy sources: tides, the Sun, heat inside the Earth, and biomass.
Rules to remember
- absolute potential energy at distance r from the Earth's centre: U = −GMm/r (at the surface, U = −GMm/R)
- escape velocity: ½mvesc2 = GMm/R, so vesc = √(2GM/R) = √(2gR)
- for the Earth, vesc is about 11.2 km s−1, and it is the same for every mass
- tidal energy: the gravitational pull of the Moon (and Sun) raises and lowers sea water, which can drive turbines
- solar energy: sunlight is used directly for heating or turned into electricity by solar cells
- geothermal energy: heat from hot rocks and molten material inside the Earth
- biomass: plant and animal waste; decay of dung in a digester gives biogas, which is mainly methane
Common mistake
Students mix up escape velocity √(2gR) with the orbital velocity close to the Earth √(gR), which is 7.9 km s−1. Escape velocity is √2 times larger, about 11.2 km s−1.
Worked example
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