Doubts about Gravitation and Force

In summary, the conversation discusses various concepts in physics such as Kepler's constant, circular motion, force and acceleration, Newton's theory of gravitation, the calculation of acceleration due to gravity, and the estimation of the mass of a double star. The concept of center of gravity is also mentioned and it is explained how it was first observed and then later verified through scientific theories. There is also a mention of Einstein's theory of general relativity as a modern approach to calculating gravitational forces. However, there is no evidence of who first discovered the concept of center of gravity.
  • #1
rktpro
62
0
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. :rolleyes:

Thanks for reply!
 
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  • #2
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
Lsos said:
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.

What I want to know is how? How it was calculated that there is something like center of gravity?
 
  • #4
rktpro said:
What I want to know is how? How it was calculated that there is something like center of gravity?

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

rktpro said:
How is acceleration equal to v^2/r in case of circular motion?
Google: uniform circular motion
rktpro said:
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?
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.
rktpro said:
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?
He invented integral calculus to do that.
rktpro said:
What are the latest and advanced means to calculate the value of acceleration due to gravity?
Modern theory of gravitation is Einstein's General Relativity.
rktpro said:
How do we estimate mass of a double star?
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.
 
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  • #6
rktpro said:
What I want to know is how? How it was calculated that there is something like center of gravity?
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
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
rktpro said:
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?
If you're curious about the history of mathematics then study it. There are many texts on the subject.
 
  • #9
jambaugh said:
If you're curious about the history of mathematics then study it. There are many texts on the subject.

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
rktpro said:
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.

http://www.cshpm.org/links/History_of_Mathematics_References2.pdf

But you have web access since you're here. Start googling e.g. "Isaac Newton" and "history of calculus". Also for info on center of mass/gravity you might research ancient building techniques. A mason must understand center of gravity in order to build structures which don't fall down or tip over.
 

1. What is the difference between gravitation and force?

Gravitation is a natural phenomenon in which objects with mass are attracted to one another. Force, on the other hand, is a push or pull that can cause an object to move or change its state of motion.

2. How does gravity affect objects on Earth?

Gravity is the force that keeps objects on Earth from floating off into space. It pulls objects towards the center of the Earth, which is why we feel like we are being pulled towards the ground.

3. Why do some people doubt the existence of gravity?

Some people may doubt the existence of gravity because it is not something that can be seen or directly observed. However, its effects can be observed and measured through experiments and observations.

4. Is there any evidence to support the theory of gravity?

Yes, there is a wealth of evidence that supports the theory of gravity. The most famous is Sir Isaac Newton's law of universal gravitation, which explains the relationship between the masses of two objects and the force of gravity between them. Additionally, Albert Einstein's theory of general relativity provides a more complete understanding of gravity and its effects on the universe.

5. Can gravity be manipulated or controlled?

As far as we know, gravity cannot be manipulated or controlled. It is a fundamental force of nature and is not something that can be altered or changed by humans. However, we can use our understanding of gravity to develop technologies such as rockets and satellites that can overcome its effects to some extent.

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