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Gravitational mass :- "weight"
You're floating in space - say about 2 million kilometers away from Earth (in a spacesuit).
You might have body mass "weighing"
link01 say 0.1 kg, a couple of ounces!
*Note
But if you came closer, to half that distance, you'd "weigh" FOUR
times link02
as much - 0.4 kilos (about one whole pound - great hey?)
That's because "gravity" follows `inverse-square law'.
Just like an exploding ice-cream factory link03 - 10 meters away you catch 1 gallon of icecream in a pail, but at 20 meters - at twice the distance - you can only catch 1/4 gallon in the same pail: the effect has diminished to a quarter.
"Center of gravity"
And here's where one misunderstanding comes in.
Above, you've seen that getting closer to a planet, say halving the distance, will increase your `weight' fourfold.
The scientists have a formula to say the same thing. It looks like this
Weight =
Earth's mass × person's mass
-------------------------
square of distance between "centers of gravity"
or
m1m2 /divided by d2
(where d is the distance to the Earth's center)
So `weight' increases as distance
decreases? Yes
BUT
that formula doesn't work all the way to the Earth's center of gravity!
You - the astronaut - will gain `weight' as you get closer to Earth's surface.
Once you're there - on top of the `ground' - you'll `weigh' maybe around 60 or 70 kilos (or so?) - and that's about as heavy as you're going to get.
If, protected against heat and pressure, you descend into the Earth, towards that center of gravity - you start weighing less again!
Halfway down (cherry colored figure) you 're surprised to see you weigh only 40 kilos or so.
Why?
Because you're putting mass link04 behind you as you dig down. And that mass has an effect - called `gravity' or `gravitational attraction' !
And if you dig on down to the center of gravity - WOW - you weigh nothing at all!
That's even less than when you were way out in space!
So, at Earth's center of gravity - there is no `gravity' ?
Well, `gravitational attraction' is all around - and equal - and so cancels out. link05
We can see there's a lot of confusing vagueness about differing meanings for the same word.
That vagueness still confuses our scientists link06
Notes:
"Weight" is how much your `inertial mass' gets pushed towards another body. It's a vector quantity.
All absolute values are only `relatively' correct as examples - Ie. the actual positions in space where you `weigh' 2 ounces (less than 0.1 kg) vary depending on direction and many are probably closer than 2 m kilometers
However, all relative ratios are `absolutely' accurate. Check with your local physics teacher
The various "masses" defined (and discussed)
The various "gravities" defined
Also see Reader's Mail 1 & Reader's Mail 2
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Reaction of mass held in rotation, or released: "Centripetal or Centrifugal Force" Reaction of mass to varying radius of rotation: "Conservation of Angular Momentum" Reaction of mass to varying angles of rotation: "Precession" Reactions of mass to other movements: "Coriolis Force" |
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