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/