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### Gravity and Acceleration

```Date: 06/24/2002 at 03:40:54
From: Alistair Quinn
Subject: Gravity

Dr. Math,

I have heard that when Astronauts lift off into space they experience
G-forces and they suddenly become really heavy. When they actually
get into space they don't weigh anything at all.

I was wondering, how fast would you have to be travelling in space to
experience 1 G-force?
```

```
Date: 06/24/2002 at 11:12:13
From: Doctor Rick
Subject: Re: Gravity

Hi, Alistair.

An astronaut in near-earth orbit (such as on the Space Shuttle) would
experience  1 G just as we do on earth (or just slightly less), if
he/she just had a place to stand that wasn't falling!

The reason an astronaut feels no gravitational force is that the
spacecraft is falling toward the earth (that's really what orbiting
is) along with the astronaut, so the spacecraft floor does not push
up on the astronaut as the ground does on us. Gravity is pulling on
both the astronaut and the spacecraft with the same 1 G-force.

On earth, if you jump off a building, then you feel no gravitational
force (you're "weightless") -- for the few seconds until you hit the
ground! (Don't try this at home.) Gravity is still pulling on you; but
you don't feel it because nothing is pushing back to keep you from
falling. Because nothing is pushing back, you ACCELERATE at 32 feet
per second per second. In other words, for each second you fall, your
SPEED INCREASES by 32 feet/second. When you first step off the
building you are not falling yet: your speed is 0 feet/second. A
second later you are falling at a speed of 32 feet/second; after
another second you are falling at a speed of 64 feet/second, and so
on.

Now suppose you are on a spacecraft out in space, whose engine is
running, with enough force to ACCELERATE you at this same rate: 32
feet/second per second. Then the floor pushes up on you with the same
force that you feel on earth: 1 G-force.

You can see this by putting that spacecraft just off the surface of
the earth, pointing up. If you didn't have the engine on, then the
rocket would fall with an acceleration of 32 feet/second per second.
Turn the engine on, and the acceleration it produces is just enough
to keep the rocket from falling. It's just as if the rocket was on
the launch pad, and you were sitting on the surface of the earth. The
force you'd feel is just the force you feel everyday from gravity: 1
G-force. And that's the same force you'd feel if you were somewhere
out in space, with the rocket exerting the same force.

Now if the rocket exerts twice as much force, it moves UP with an
acceleration of 32 feet/second per second. You feel 1 G from gravity
and a second G-force from the acceleration of the rocket: you feel
twice as heavy.

When you get into orbit, you're traveling sideways to the earth's
gravity, but you don't feel that because the rocket is falling
sideways along with you. But if the rocket is still running with that
same acceleration, you'll still feel twice as heavy as you do on
earth. The rocket is accelerating at 64 feet/second per second
(because it isn't fighting gravity any more), so you feel 2 G's from
the rocket and none from gravity.

The main point is that it isn't how fast you are going that creates
the apparent gravity or "G-force". It's how fast your speed is
CHANGING. At an acceleration of 32 feet/second per second (or "32
feet per second squared"), you experience a force equal to that of
gravity, or 1 G.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Physics/Chemistry

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