SUMMARY
The calculation of galactic mass as a function of radius is established through the equations M(r)=v²r/G and M(r)=vrc²/G, with the former being the correct formulation for determining mass based on velocity and radius. The velocity, v, can be derived from the flat rotation curve of the galaxy, allowing for the calculation of mass using M(r)=Mr/R, where M is the total mass and R is the radius. For tidal force calculations, the formula r=(d³m/(2MR))¹/² is used to determine the distance at which a star is tidally disrupted by a nearby galaxy, where m is the total mass of the galaxy containing the star, R is its radius, M is the mass of the nearby galaxy, and d is the distance between their centers.
PREREQUISITES
- Understanding of Newton's law of gravitation
- Familiarity with galactic dynamics and rotation curves
- Knowledge of tidal forces in astrophysics
- Proficiency in algebraic manipulation of equations
NEXT STEPS
- Study the derivation of the rotation curve for spiral galaxies
- Learn about the application of Newtonian gravity in astrophysical contexts
- Explore tidal disruption events and their implications in galaxy interactions
- Investigate the use of computational models for simulating galactic dynamics
USEFUL FOR
Astronomers, astrophysicists, and students studying galactic dynamics or tidal interactions in astrophysics will benefit from this discussion.