• Question: when does gravity become weak enough from earth that we'd float away ?

    Asked by baeby to Chris, Josh, Rebecca, Rob, Susan on 22 Jun 2015.
    • Photo: Rebecca Dewey

      Rebecca Dewey answered on 22 Jun 2015:

      There isn’t a limit exactly, but it depends on how fast you’re travelling. Gravity acts with a strength that depends on your mass and your distance from the centre of the Earth. In order to pull you to Earth, the force acting on you from gravity would have to be strong enough to stop you moving away, and start you moving back to earth. Escape velocity is the minimum speed you need to be travelling at so that Earth’s gravity will not pull you back down.

    • Photo: Susan Cartwright

      Susan Cartwright answered on 22 Jun 2015:

      Gravity is an inverse square law: if you go twice as far away, the force of gravity is four times less.

      If the Earth were on its own in deep space, there would NEVER be a distance at which you would float AWAY from the Earth – if you were stationary, there would always be some force pulling you towards the Earth. The further away from Earth you were, the smaller that force would be.

      The Earth is not on its own in deep space, but in orbit around the Sun. So there comes a point as you move away from the Earth where the Earth’s gravity loses out to the Sun’s. This distance is roughly 260000 km. If you were to place a stationary object more than 260000 km from the Earth, it would fall towards the Sun rather than the Earth.

      This is complicated by relative motion. The Moon is more than 260000 km from the Earth, and if you plot its path through space you will see that indeed it is always accelerating towards the Sun. But, because the Earth’s motion around the Sun and the Moon’s motion around the Sun are almost the same, from our perspective we see the Moon orbiting us as we orbit the Sun.

      To work out how fast you need to be moving outwards to escape the Earth’s gravity, compare the gravitational potential energy, -GMm/r (where M is the Earth’s mass, m is your mass, and r is your distance from the centre of the Earth), with the kinetic energy, 1/2 mv^2. This gives v^2 = 2GM/r. It you are travelling outwards with that speed or higher, you will escape Earth’s gravity (though not the Sun’s). For something at the Earth’s surface, that’s a speed of about 11.2 km/s (about 25000 mph).

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