Exploring Dark Matter: The Gravitational Field Strength Within a Thin Disk

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In summary, the conversation revolves around researching dark matter and its effects on galaxy rotation curves. The problem at hand is determining the gravitational field strength (g) within a thin, flat disk with uniform mass per unit area, and how it varies with respect to the distance from the center of the disk. Resources from Google were utilized to find solutions, but most of them focused on the z-axis instead of the x-axis, which is necessary for simulating a galaxy. The individual has derived an integral to solve for g, but it resulted in an infinite value. They are willing to provide a step-by-step breakdown to identify any mistakes.
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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.
 

What is dark matter?

Dark matter is a hypothetical form of matter that is believed to make up approximately 85% of the total matter in the universe. It does not emit or absorb light, making it invisible and difficult to detect.

What is the gravitational field strength within a thin disk?

The gravitational field strength within a thin disk refers to the force of gravity exerted by the matter within a disk-shaped region in space. In the context of dark matter, it is used to understand the distribution and density of dark matter within a disk-like structure.

How is dark matter detected?

Dark matter cannot be directly detected because it does not interact with light. Instead, scientists use indirect methods such as observing the gravitational effects of dark matter on visible matter, studying the rotation curves of galaxies, and looking for evidence of dark matter collisions in particle accelerators.

Why is it important to study dark matter?

Studying dark matter is important because it makes up such a large portion of the universe and has a significant impact on the formation and evolution of galaxies. Understanding the properties and behavior of dark matter can also help us better understand the fundamental laws of physics.

What are some current theories about the nature of dark matter?

There are several theories about the nature of dark matter, including the WIMP (Weakly Interacting Massive Particles) theory, which suggests that dark matter is made up of particles that interact weakly with regular matter. Another theory is the MACHO (Massive Compact Halo Objects) theory, which proposes that dark matter is made up of massive objects such as black holes or brown dwarfs. However, none of these theories have been definitively proven and the nature of dark matter remains a mystery.

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