# Doubts about Gravitation and Force

1. Jan 25, 2012

### rktpro

My book says r^3/t^2 was found constant by Kepler. What this constant is called?

How is acceleration equal to v^2/r in case of circular motion?

Why is rate of change of momentum or say product of mass and acceleration equal to force? Why not was it ma^2? How was it proved that it is equal to ma?

How newton showed that a spherical body of uniform density behaves as if whole of its mass is concentrated at its center? Also, why is it that a symmetrical body of perfect density balances about the point of center of gravity?

What are the latest and advanced means to calculate the value of acceleration due to gravity?

How do we estimate mass of a double star?

These questions remain unanswered in my book. Maybe because they are little tough to understand.

Please keep the replies as simple as you can so that I have no problem in understanding them.

2. Jan 26, 2012

### Lsos

The first few questions are very easy and cheap to check by experiment. The fact is that if you push twice as hard, a mass will accelerate twice as fast (and not any other value). Also the fact is that you can balance a mass by holding it at a point directly below its center of gravity. Again, very easy to check for yourself.

So that's my answer to your questions...it has been checked literally countless times and never has the result been any different than what the equations say.

As for the value of gravity, I don't know how they check it but it's my understanding that it's one of the least certain values of a universal constant that we have.

3. Jan 26, 2012

### rktpro

What I want to know is how? How it was calculated that there is something like center of gravity?

4. Jan 27, 2012

### Lsos

I guess I don't know. A nice way of finding center gravity is to suspend an object with a string, but from two different locations. The point where the strings intersect is the center of gravity.

I imagine a long time ago, someone tried to hang something by a string and found that one point in the object would always be directly below the string. Since this is a good thing to know (especially when you want to hang something....chandelier, picture, swing, person...anything), someone gave it a name and figured out how to find it mathematically. Surely someone also noticed that this is a good thing to know when you want to balance something.

Ultimately I'm not sure, but it seems like a simple enough concept that I wouldn't be surprised if it has been lost to history (like the inventor of the wheel).

5. Jan 27, 2012

### mathfeel

Kepler did not really named this constant. Under Newton's law, this proportionality constant is G M, where G is a universal constant, and M is the mass of the star (not exactly, but close enough when mass of star >> mass of planet). You can check that G M has the correct dimension. So this is constant in our solar system. In another system with a different star mass, it'd have a different value. G, on the other hand, is UNIVERSAL.

It is not some mathematics that you can prove. Essentially, it is the definition of inertial mass: the property of matter that is the proportionality factor between applied force and acceleration.
He invented integral calculus to do that.
Modern theory of gravitation is Einstein's General Relativity.
If you can measure how far apart they are and how fast is their orbital period, apply gravitation theory. Actually, this only gives you the reduced mass.

Last edited: Jan 27, 2012
6. Jan 27, 2012

### jambaugh

One does not calculate that there is something like center of gravity, one verifies it empirically. Take a block of wood, set it on a tray with some sandpaper to keep it from sliding, tilt it until it tips. Find the vertical line above the corner where it just starts tipping. Do this at all angles and you'll see all these vertical lines pass through a common point. Call this point the center of gravity.

THEN once you observe the existence of this you develop theories of gravity and see which ones allow you to calculate the correct center of gravity.

That's science!!!

7. Jan 27, 2012

### rktpro

Is there a historical evidence that first centre of balance or something was discovered and then Newton showed up with his calculus and found centre of gravity?

8. Jan 28, 2012

### jambaugh

If you're curious about the history of mathematics then study it. There are many texts on the subject.

9. Jan 28, 2012

### rktpro

Can you please name a few because I doubt they would be available in the small library we have in town. I would buy them online.

10. Jan 30, 2012