What Is the Gravitational Field Strength Within a Uniform Thin Disk?

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SUMMARY

The gravitational field strength (g) within a uniform thin disk is determined by the area density (δ) and the radius (R) of the disk. The discussion highlights the need to focus on the x-axis rather than the z-axis for simulations related to galaxy rotation curves. An integral approach is suggested to calculate g, but the author encounters an issue where the value becomes infinite, indicating a potential error in the setup of the integral. The discussion references several Physics Forums threads for additional context and methodologies.

PREREQUISITES
  • Understanding of gravitational field strength and its mathematical representation
  • Familiarity with integral calculus, particularly in physics applications
  • Knowledge of area density (δ) and its role in gravitational calculations
  • Basic concepts of galaxy rotation curves and dark matter implications
NEXT STEPS
  • Study the derivation of gravitational field strength for uniform mass distributions
  • Learn about the mathematical treatment of integrals in gravitational physics
  • Research the effects of dark matter on galaxy rotation curves
  • Explore alternative methods for simulating gravitational fields in astrophysics
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Astronomy researchers, astrophysicists, and students studying gravitational physics, particularly those interested in dark matter and galaxy dynamics.

tade
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I'm researching dark matter and how it affects galaxy rotation curves, I came up with the problem below.

Imagine a very thin, flat disk which has uniform mass per unit area.

What is the gravitational field strength (g) within the disk itself? How does g vary with respect to r, the distance from the center of the disk.

The area density of the disk is δ and the radius of the disk is R.
 
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Most of the threads focus on the z-axis. But in order for me to simulate a galaxy, I have to focus on the x-axis.


I came up with an integral to find the value of g, but its value ends up being infinite.

I can write it down step-by-step to let you guys find out where I went wrong.
 

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