Equation (Chandrasekhar, Newton's Principia)

  • Thread starter Poetria
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In summary: Indeed he does use modern notation. And in the precedent chapter he employs the same sign with vectors. In addition, he refers to the concept of versed sine, which is little used but fortunately I have found a good definition.I have also found "A History of Vector Analysis." :) Thank you very much. It is tough stuff. :)
  • #1
Poetria
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Homework Statement



I am reading a book by Chandrasekhar, "Newton's Principia for a Common Reader." I don't understand some notation.

Homework Equations



(2) A(1)S(1) x A(1)D(1)=(A(1)B(1))^2

What does x means here? A cross product? Could you give me a hint where to find a good introduction to these geometrical operations? Obviously, there is a gap in my background.
 

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  • #2
Poetria said:

Homework Statement



I am reading a book by Chandrasekhar, "Newton's Principia for a Common Reader." I don't understand some notation.

Homework Equations



(2) A(1)S(1) x A(1)D(1)=(A(1)B(1))^2

What does x means here? A cross product? Could you give me a hint where to find a good introduction to these geometrical operations? Obviously, there is a gap in my background.

It looks like a simple "times" = "multiplication" sign.
 
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  • #3
Ray Vickson said:
It looks like a simple "times" = "multiplication" sign.

Oh, ok. I am overegging the pudding then. :) Many thanks. :) Sometimes he doesn't use it you know.
 
  • #4
Poetria said:
Oh, ok. I am overegging the pudding then. :) Many thanks. :) Sometimes he doesn't use it you know.

Just for future reference: the × sign could not be a cross-product, because that would give you an equation with a vector on one side and a scalar on the other. Besides, Newton wrote Principia hundreds of years before the invention of vectors and cross-products, etc (although, of course, maybe Chandraskhar is using modern notation and concepts in writing about Newton's work).
 
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  • #5
Ray Vickson said:
Just for future reference: the × sign could not be a cross-product, because that would give you an equation with a vector on one side and a scalar on the other. Besides, Newton wrote Principia hundreds of years before the invention of vectors and cross-products, etc (although, of course, maybe Chandraskhar is using modern notation and concepts in writing about Newton's work).

Indeed he does use modern notation. And in the precedent chapter he employs the same sign with vectors. In addition, he refers to the concept of versed sine, which is little used but fortunately I have found a good definition.
I have also found "A History of Vector Analysis." :)
Thank you very much. It is tough stuff. :)
 

1. What is the equation developed by Chandrasekhar in relation to Newton's Principia?

The equation developed by Chandrasekhar in relation to Newton's Principia is known as the Chandrasekhar limit. It is a mathematical formula that determines the maximum mass of a white dwarf star, beyond which it will collapse and form a black hole.

2. How was the Chandrasekhar limit derived?

The Chandrasekhar limit was derived by Subrahmanyan Chandrasekhar in 1931. He used Newton's principles of gravity and motion to formulate an equation that takes into account the effects of quantum mechanics on the behavior of matter in a white dwarf star.

3. What is the significance of the Chandrasekhar limit?

The Chandrasekhar limit is significant because it provides a maximum threshold for the mass of a white dwarf star. It helps us understand the life cycle of stars and the formation of black holes. It also has implications for the study of supernovae and the evolution of galaxies.

4. How does the Chandrasekhar limit relate to other fundamental constants?

The Chandrasekhar limit is dependent on the Planck constant, the gravitational constant, and the speed of light, making it a fundamental constant in astrophysics. It also relates to other important concepts such as the Schwarzschild radius and the Eddington limit.

5. Has the Chandrasekhar limit been observed in real-life scenarios?

Yes, the Chandrasekhar limit has been observed in various astronomical observations. For example, the mass of a white dwarf star in the binary system known as V617 Sagittarius was found to be very close to the predicted Chandrasekhar limit. This provides strong evidence for the validity of the equation developed by Chandrasekhar.

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