What is the Gravity Equation for Understanding Mass and Black Holes?

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Discussion Overview

The discussion revolves around the gravity equation in the context of understanding mass and black holes. Participants explore the calculations involved in gravitational attraction and the conditions necessary for an object to become a black hole, touching on both classical and relativistic perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the gravity equation and how to calculate the acceleration towards a massive object, specifically in the context of black holes.
  • Another participant provides Newton's law of gravitation and discusses its limitations in strong gravitational fields, emphasizing the need to consider the distortion of space-time geometry.
  • A participant points out a potential error regarding the factor of 2 in the Schwarzschild radius formula and references classical equations for gravitational acceleration.
  • A later reply acknowledges the correction regarding the Schwarzschild radius and updates the original post accordingly.

Areas of Agreement / Disagreement

Participants generally agree on the need to consider both Newtonian and relativistic approaches to gravity, but there is a disagreement regarding the correct formulation of the Schwarzschild radius, which was later corrected by one participant.

Contextual Notes

The discussion includes assumptions about the applicability of Newton's law in different gravitational contexts and the need for clarity on the definitions of terms like Schwarzschild radius. There are unresolved aspects regarding the implications of these equations in extreme conditions, such as near black holes.

Who May Find This Useful

This discussion may be useful for individuals interested in gravitational physics, black hole theory, and the mathematical formulations of gravity.

Gamish
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Gravity equation?

I have a question, after reading about black holes. What is the "gravity equation"? Let me explain. If the Earth had a weight of 1000000000 KG, how fast would I accelerate to that object, if I was 1 KM away from it or something? Do you get my point, I don't know all the technical apsects, I am just trying to figure out how massive an object has to be to open up aa black hole.

Thanks in advanced :)
 
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You can use Newton's law, F = GmM/r^2, to calculate the force of attraction between two bodies that are far away from each other.

G is the universal gravitational constant, m and M are the two masses, and r is the distance between them.

For strong gravitational fields this equation doesn't work, but I don't think there is any model of gravity "as a force" that will work. The problem is that the geometry of space-time itself becomes distorted near a sufficiently dense mass, so that thinking of gravity as a "force" will not give the correct answer without taking the distortion of the geometry into account.

The event horizon of a black hole occurs at radius [fix] r = 2GM/c^2, called the Schwarzschild radius. Here G is the same universal gravitational constant as it was in Newton's law of gravity, M is the mass of the massive body, and c is the speed of light. For a body as massive as the Earth's sun, the Schwarzschild radius is 1.5km.
 
Last edited:
Not to be a grinch, but I think you are short a factor of 2 in your Schwarzschild radius.

Galileo's constant acceleration g due to gravity came out nicely from Newton's theory as g = GMp/(Rp^2) where Mp is the mass of a spherical planet of radius Rp. Have a look at Kip Thorne's paper back on black holes or Wheeler & Taylor's book on black holes.
 
You are (of course) quite right about the factor of 2 - I fixed the original post to reflect the correct formula for the Schwarzschild radius.

Merry xmas & a happy new year
 

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