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The equivalence principle

Space and time · level 8, lesson 1 of 6

A question to start

You wake up in a closed room with no windows. You feel your weight as if you were on Mars. Could you be in a rocket far out in space instead? Is there any experiment that could tell?

The idea

Einstein noticed something simple: a person falling freely feels no weight. Astronauts on a space station are not out of reach of Earth's gravity; they are falling round the Earth all the time, and so they float.

The equivalence principle says that, in a small enough room, the effects of gravity and of acceleration are exactly the same. A rocket accelerating at 3.73 m/s² feels just like standing on Mars. No experiment inside the room can tell them apart.

That only works if everything falls at the same rate, whatever it is made of. The MICROSCOPE satellite tested this in orbit from 2016 to 2018, dropping pairs of test masses made of different metals. Its final result, in 2022, found no difference to about one part in 10¹⁵.

From this, Einstein built general relativity: gravity is the curving of space and time, and falling bodies simply follow the straightest paths through it.

Feels the same as standing on Mars Earth
A rocket accelerating at 3.73 m/s² 9.82 m/s²
on Marsrocket, 3.73 m/s² up

Worked examples

1. Mars in a rocket. To feel Mars gravity in deep space, the rocket must speed up by 3.73 m/s every second.

2. Floating in orbit. A space station 400 km up still feels about 90% of surface gravity. Its crew float because they and the station fall together.

3. The MICROSCOPE limit. One part in 10¹⁵ is like weighing two 1,000-tonne loads and finding them equal to within a millionth of a gram.

Try it

  1. State the equivalence principle in your own words.
  2. Why do astronauts in orbit float?
  3. What did MICROSCOPE test, and what did it find?
  4. A rocket accelerates at 9.82 m/s². What does it feel like inside?
Answers
  1. In a small closed room, the effects of gravity cannot be told apart from those of acceleration.
  2. They are falling freely, together with their station.
  3. Whether bodies of different materials fall at the same rate. They do, to about one part in 10¹⁵.
  4. Like standing on Earth.

Common mistake

"There is no gravity in orbit." Gravity at the height of a space station is nearly as strong as on the ground. Weightlessness comes from falling, not from escaping gravity.

Where it leads