Works of Riemann related to Astronomy that I can understand?

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SUMMARY

Bernhard Riemann's development of Riemannian geometry is foundational to general relativity, which addresses the limitations of Newton's laws at astronomical distances. This geometry is essential for understanding Einstein's theories, particularly in the context of special relativity and concepts like Lorentz contraction. Riemann's work allows for a geometric interpretation of gravitational phenomena, making it relevant to astronomical applications. The discussion emphasizes the importance of Riemannian geometry in modern physics without delving into tensor calculus.

PREREQUISITES
  • Understanding of Riemannian geometry
  • Basic knowledge of general relativity
  • Familiarity with special relativity concepts
  • Awareness of Newtonian physics limitations
NEXT STEPS
  • Research the implications of Riemannian geometry in general relativity
  • Study the Lorentz contraction and its significance in special relativity
  • Explore the historical context of 19th-century mathematics and its influence on astronomy
  • Examine the relationship between geometry and physics in the context of astronomical phenomena
USEFUL FOR

Students of mathematics and physics, historians of science, and anyone interested in the intersection of Riemann's work and astronomical theories.

benorin
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Looking for a connection to astronomy for a history of mathematics report on 19th century mathematicians. I don't do astronomy. Would like to know of any mathematical developments of Riemann that are used in astronomy that I can understand (which expressly excludes any thing with the word tensor in it.) Don't work to hard on it (I have google too,) just thought you guys would know.

TIA,

Benorin
 
Astronomy news on Phys.org
Bernhard Riemann developed Riemannian geometry. This is used through out general relativity. Newton’s laws didn't work at very large (astronomical distances), that is why we use GR. Einstein wouldn't of been able to develop his theories in Euclidean geometry.
 
Is there any connection between Riemann geometry and special relativity, that subject is within my mental grasp. Perhaps the Lorentz contraction?
 
http://www.superstringtheory.com/basics/basic2a.html, read the section on relativity and geometry.
 

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