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Escaping

Gravity and orbits · level 4, lesson 6 of 6

A question to start

Throw a ball up: it comes back. Throw harder: it goes higher, but still comes back. Is there a speed so fast that it never comes back at all?

The idea

Yes. As a ball climbs, gravity slows it. But gravity also gets weaker the higher it goes (the inverse square rule). If the ball starts fast enough, gravity weakens so quickly that it can never quite stop the ball. The ball slows down forever but never turns round. It has escaped.

The smallest speed that does this is the escape speed. It depends on the planet's mass and size.

World Escape speed from the surface In km/h
Earth 11.2 km/s about 40,000
Mars 5.0 km/s about 18,000
Moon 2.4 km/s about 8,500
Phobos about 11 m/s about 40

Escaping Mars needs less than half the speed of escaping Earth. Since the fuel a rocket needs grows very fast with the speed it must reach, that makes a huge difference: leaving Mars is far easier than leaving Earth. It is one reason people talk about building ships and fuel on Mars, or on its moons, instead of lifting everything from Earth.

On Phobos, the escape speed is about 40 km/h: a fast bicycle. A strong throw, or a careless jump, could send something off Phobos for good.

In real life, a rocket does not fire once and coast up: it keeps pushing for many minutes. And going into orbit needs less speed than escaping: about 7.8 km/s for low Earth orbit, 3.5 km/s round Mars. Escape speed is for the thing that leaves the planet altogether.

Worked examples

1. Comparing. \(11.2 \div 5.0 \approx 2.2\): escaping Earth takes 2.2 times the speed of escaping Mars.

2. A ball on Phobos. A good throw is about 25 m/s (90 km/h). That is more than twice Phobos's escape speed, so the ball would leave Phobos forever, and go into orbit round Mars.

Try it

  1. What is escape speed?
  2. Which has the larger escape speed, Earth or Mars? About how many times larger?
  3. Could you throw a ball off Phobos? Explain.
  4. Why does a rocket going to orbit need less speed than escape speed?
Answers
  1. The smallest speed something must start with to never come back, without any more push.
  2. Earth: 11.2 km/s against 5.0 km/s, about 2.2 times larger.
  3. Yes: escape speed is only about 11 m/s, slower than a good throw.
  4. In orbit it is still held by the planet, falling round it; it does not need to leave altogether.

Common mistake

"Escaping means getting out of gravity." Gravity never ends. Escaping means going fast enough that gravity, getting weaker and weaker, never manages to pull you back.

Where it leads