Gravitational difference between a black hole and a star

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SUMMARY

The discussion clarifies the gravitational differences between a stellar-mass black hole and a stellar-mass star, specifically using Newtonian gravity principles. The formula F=Gm/r² illustrates that while both objects may have the same mass, the black hole's significantly smaller size results in a stronger gravitational field at its surface. This increased density leads to the ability of the black hole to trap light, unlike a star such as the Sun, which cannot due to its larger radius and lower surface gravity.

PREREQUISITES
  • Understanding of Newtonian gravity and the formula F=Gm/r²
  • Knowledge of stellar-mass black holes and their properties
  • Familiarity with concepts of density and gravitational fields
  • Basic principles of light behavior in gravitational fields
NEXT STEPS
  • Research the properties of black holes, focusing on event horizons and singularities
  • Study the implications of gravitational lensing and light behavior near massive objects
  • Explore advanced gravitational theories, such as General Relativity
  • Investigate the relationship between mass, density, and gravitational force in astrophysics
USEFUL FOR

Astronomy students, physicists, and anyone interested in understanding the fundamental differences in gravitational effects between black holes and stars.

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How come the gravity of a stellar- mass black hole is strong enough to trap light but the gravity of a stellar-mass star (eg the sun) is not strong enough to trap light ?
 
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This question is easier to think about if you start with ordinary classical Newtonian gravity: ##F=Gm/r^2## is the formula for the strength of the gravitational field at a distance ##r## from the center of a spherical object (like a star) with mass ##m##. So if we have two objects with the same mass, but one of them is much denser (so is much smaller) than the other, what does that tell us about the strength of the gravitational force at the surface?
 
Thankyou Nugatory. I think that your marvellous formula tells me that the strength of the gravitational force is greater at the surface of the smaller object compared to a larger object with the same mass.

Doesn't that mean that the smaller object has stronger gravity ?
 
Tatest said:
Doesn't that mean that the smaller object has stronger gravity ?
It means that the gravitational field is stronger at the surface of the smaller object, because the surface is closer to the center.

You can attach the words "the smaller object has stronger gravity" to this fact if you want, but not everyone is going to understand those words the same way. The math is precise and unambiguous, and that's part of why mathematics is the language of physics.
 

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