Doubts about Gravitation and Force

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Discussion Overview

The discussion centers around various questions related to gravitation and force, including historical perspectives, mathematical definitions, and empirical observations. Participants explore concepts such as Kepler's laws, Newton's principles, and the calculation of gravitational constants, as well as practical applications and historical context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Historical

Main Points Raised

  • One participant inquires about the constant found by Kepler in relation to r3/t2 and its naming.
  • Questions are raised regarding the relationship between acceleration, velocity, and radius in circular motion, with a suggestion to search for information on uniform circular motion.
  • Participants discuss the definition of force as the product of mass and acceleration, questioning why it is not expressed as ma2.
  • There is mention of how Newton demonstrated that a spherical body of uniform density behaves as if its mass is concentrated at its center, with a reference to integral calculus.
  • Inquiries are made about modern methods for calculating acceleration due to gravity and estimating the mass of double stars.
  • One participant describes an empirical method for verifying the existence of a center of gravity by observing tipping points of objects.
  • Historical questions arise regarding the discovery of the center of balance before Newton's contributions, with suggestions to explore historical texts on mathematics.

Areas of Agreement / Disagreement

Participants express varying degrees of certainty about the empirical verification of concepts like the center of gravity and the historical development of these ideas. Some participants provide experimental methods while others focus on theoretical aspects, indicating that multiple views and uncertainties remain in the discussion.

Contextual Notes

Participants reference the historical context of mathematical discoveries and the empirical basis of physical concepts, but there are no definitive conclusions drawn about the historical timeline or the development of these ideas.

Who May Find This Useful

This discussion may be of interest to those studying physics, mathematics, or the history of scientific concepts, as well as individuals curious about the empirical foundations of gravitational theory and force.

rktpro
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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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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.
 
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?
 
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).
 
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.
 
Last edited:
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!
 
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?
 
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.
 
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.
 

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