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Author Topic: Centers of Gravity/Mass  (Read 7709 times)

Offline Brex

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« on: 10/02/2008 20:38:14 »
I recall from sometime in my past a probable statement of fact that a center of gravity and its associated center of mass do not always coincide. I cannot remember if the reason was given but presume that a case could occur with orbiting masses such as the earth moon relationship. If any reader could confirm or deny these thoughts perhaps including the whereabouts of the center of rotation and the null gravity point between the bodies I would be quite happy.


 

Offline syhprum

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« Reply #1 on: 10/02/2008 20:46:27 »
As far as I recall the centre of gravity of the Earth/Moon system is about 2000Km below the surface of the Earth
 

Offline JimBob

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« Reply #2 on: 11/02/2008 00:53:22 »
... and growing slowly larger. The moon is moving slowly away from the earth.
 

Offline Saganist

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« Reply #3 on: 11/02/2008 04:34:28 »
Hi guys,

The points of equilibrium in gravity between earth, moon and sun are the Lagrange points. I guess a Google lookup on these would provide the answer as to their exact locations. Also, I would guess there's more than one cares to know in the Wikipedia explanations, which can be incredibly detailed on physics subjects.

As for the difference between center of gravity and center of mass, I was not aware of such a difference. Sounds interesting if there is.

The mass of objects is due to their constituent particles aquiring mass via the Higgs mechanism, whereas the force of gravity is conveyed by the graviton and its interactions.

The center of gravity would be the point from which gravity force vectors radiate.

The center of mass is somewhere between the sermon and communion.  ;D

Cheers.

Saganist
 

lyner

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« Reply #4 on: 11/02/2008 10:20:12 »
As per usual, I will give the classical, textbook, view; an important starting point.
The Centre of Mass  of an object or a set of objects is an actually defined point.
Assume,  for simplicity, that there are two masses, small enough to regard as points.
For two masses M1 and M2, the CM  lies on a line between the two masses at distances D1 and D2, respectively, from the masses such that
M1.D1 = M2.D2
That equation is the same as you use for working out 'moments' with levers in school, remember. When the fulcrum is in the right place, the moments are balanced (equal and opposite).
The CM is the point  where you could place a mass  of M1+M2 and, for a distant third, point,  mass, the gravitational attraction would be the same as for the two separate masses.
You can extend this to any number of points or  the distributed mass of a real sized object if your maths is up to it.

The CM is often called the Centre of Gravity because, for objects on the Earth's surface, the CM is where Earth's gravity can be thought of as acting.  CG isn't really the proper term to use in other circumstances, though.
Imagine the Earth and the Moon, as a pair of masses. If you are on the Earth, the place where the gravity of the two objects acts on you (the CG) is, definitely, pretty much downwards - near  the centre of the Earth. If, however, you are on the surface of the Moon, the place that the effective gravity of the two masses acts on you (the CG, again) is 'downwards' -i.e. near the centre of the Moon.
So this 'centre of gravity' is in different places, depending on where you are looking from; it is dominated by the closer masses. Hence, it is a rather woolly term to use.
Why does the CG of an object appear to be the same as the CM on Earth? It's because the Earth is big enough to seem flat for most objects and the gravitational 'lines of force' are virtually, parallel ('vertical') - as if the Earth were at infinity.


« Last Edit: 11/02/2008 10:25:01 by sophiecentaur »
 

Offline DoctorBeaver

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« Reply #5 on: 11/02/2008 18:48:46 »
Quote
The center of mass is somewhere between the sermon and communion.

 

Offline DoctorBeaver

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« Reply #6 on: 11/02/2008 18:54:33 »
sophiecentaur - That's very interesting.

I used to ride motorbikes and always preferred American & European bikes because, as we would say, the centre of gravity was lower (Japanese bike manufacturers have since learned their lesson and shifted the centre lower). Were we wrong in saying that? Should we have said "the centre of mass"?
 

lyner

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« Reply #7 on: 11/02/2008 19:02:54 »
Yes, but it would be a brave man, in the company of a load of hairy bikers, to get pedantic about Physics!

CM would be particluarly correct because you would be really considering the effect of cornering, where it's Mass X Radial Acceleration X distance above the ground of the CM that tips you over.
 

Offline DoctorBeaver

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« Reply #8 on: 11/02/2008 19:08:42 »
Yes, but it would be a brave man, in the company of a load of hairy bikers, to get pedantic about Physics!

 :D
 

Offline Brex

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« Reply #9 on: 12/02/2008 11:03:31 »
Thanks for the replies.

I found figures for Earth mass (597.42x10˛˛), Moon mass (7.3483), mean distance between (384,392 km) and equatorial Earth diameter (12,756km). My pretty elementary calculations, based on the reminder from Sophiecentaure, tell me that the centre of mass lies 4,670 km from earth centre. Pretty close to the round figure remembered by syhprium.

I was actually curious about the location of the centre of mutual Earth Moon orbits and now presume that that is it. I had imagined it to be somewhere between the two bodies.

 

Offline Brex

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« Reply #10 on: 12/02/2008 11:15:14 »
Correction - 1678km from earth centre. Sorry
 

Offline Brex

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« Reply #11 on: 12/02/2008 11:18:16 »
Wrong again. Right the first time. Why don't I check what I'm writing????
 

Offline Saganist

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« Reply #12 on: 13/02/2008 07:03:46 »
Hi Brex,

sc has it pretty much right.

Found this via Google search:

newbielink:http://en.wikipedia.org/wiki/Center_of_mass [nonactive]

and, of many links for this title:

newbielink:http://72.14.205.104/search?q=cache:ZhPDDM0Oe8cJ:ruina.tam.cornell.edu/Book/COMRuinaPratap.pdf+%22center+of+mass%22&hl=en&ct=clnk&cd=6&gl=ca [nonactive]

On page 5 begins the section on center of gravity. By page 7, is found the statement:

"The words ‘center of mass’ and ‘center of gravity’ both describe the same point in space."

Cheers.

Saganist
« Last Edit: 13/02/2008 07:12:52 by Saganist »
 

Offline Saganist

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« Reply #13 on: 13/02/2008 07:19:46 »
Hi Brex,

Found this on Lagrange points:

newbielink:http://www.space.com/php/popup/lagrange/lagrange3.html [nonactive]

Cheers.

Saganist
 

lyner

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« Reply #14 on: 13/02/2008 09:09:17 »
Hi Brex,

Found this on Lagrange points:

www.space.com/php/popup/lagrange/lagrange3.html

Cheers.

Saganist
Nice animation but I wonder whether it would be any easier to put an asteroid (i.e. less energy involved) in the stable Lagrangian points than to put it in any other orbit around Earth at a similar distance. Would its actual location in an LP actually be an advantage? The potential well in the vicinity of the LP is very shallow.
 

Offline Brex

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« Reply #15 on: 16/02/2008 14:47:19 »
Hi Brex,

Found this on Lagrange points:

newbielink:http://www.space.com/php/popup/lagrange/lagrange3.html [nonactive]

Cheers.

Saganist
Nice animation but I wonder whether it would be any easier to put an asteroid (i.e. less energy involved) in the stable Lagrangian points than to put it in any other orbit around Earth at a similar distance. Would its actual location in an LP actually be an advantage? The potential well in the vicinity of the LP is very shallow.
 


At, what I think is, a pretty good guess (I've forgotten even the basics of the Calculus), the Lagrangian points lie on the Moon's orbit at a point where the lunar and the earth gravities give a resultant attraction from their centre of mass. They would be the only two stable orbital points anywhere near the lunar orbit.
 

lyner

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« Reply #16 on: 16/02/2008 15:07:35 »
Quote
They would be the only two stable orbital points anywhere near the lunar orbit.
You are suggesting that station-keeping could be achieved for free, I presume. Apart from that, would there be any advantage? You would still have to get there.
 

Offline Brex

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« Reply #17 on: 17/02/2008 21:15:43 »
Apologies SS, I stand to be corrected but I was under the impression that they were called the stable lagrangian points for that reason. The other three lagrangian points are unstable and require frequent correction. I don't envisage any advantage as they are each at one apex of equilateral triangles formed with the Earth and Moon as the others.
 

lyner

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« Reply #18 on: 17/02/2008 22:49:23 »
I understand that the two stable LPs may be occupied by a certain amount of clutter already. Never know what you might find there!
 

Offline DoctorBeaver

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« Reply #19 on: 17/02/2008 23:11:25 »
I understand that the two stable LPs may be occupied by a certain amount of clutter already. Never know what you might find there!

Lord Lucan?
 

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« Reply #19 on: 17/02/2008 23:11:25 »

 

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