What is the density of matter near the sun in a 1/r^2 case?

In summary, the sun orbits the galaxy at a velocity of 220 km/s, 8500 parsecs away from the centre. To calculate the Keplerian velocity of a star at a radius of 1000 parsecs, we can use the formula v^2=(GM/R)^1/2, where M is the mass and R is the radius. If the density of matter in the galaxy follows a 1/r distribution, the velocity would be 75 km/s. However, if the density follows a 1/r^2 distribution, the velocity would remain constant at all radii. The density of matter in the vicinity of the sun in this case would be directly proportional to 1/r^2.
  • #1
Bacilla
7
0
The sun orbits the galaxy at 220 km/s at a distance of 8500 parsecs from the centre of the galaxy. If the density of matter in the galaxy drops off proportional to 1/r, what would be the Keplerian velocity of a star orbiting at a radius of 1000 parsecs? What would be the Keplerian velocity of that star if the density of matter in the galaxy drops proportional to 1/r2 ? What is the density of matter in the vicinity of the sun in this 1/r2 case?
 
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  • #2


show attempt to solution if you want to get some help, read and follow the forum rules.
 
  • #3


I have solved it using v^2=(GM/R)^1/2 and M=(4/3*3.14*R^3)1/R
If density is proportional to 1/r, the keplerian velocity at 1000 parsecs is 75km/s
And if the density is 1/r^2, then the speed is constant at all radiuses.
I Think this does make sense?
 

Related to What is the density of matter near the sun in a 1/r^2 case?

1. What is density of matter?

Density of matter refers to the amount of mass per unit volume of a substance. It is a physical property that can be used to identify and compare different materials.

2. How is density of matter measured?

Density is typically measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It can be calculated by dividing the mass of an object by its volume.

3. What factors affect the density of matter?

The density of matter can be affected by factors such as temperature, pressure, and the arrangement of particles in a substance. For example, as temperature increases, the particles in a substance may spread out, resulting in a lower density.

4. Why is density of matter important?

Density is an important property of matter because it can help identify and classify substances, and it can also be used to predict how substances will behave in different conditions. For example, substances with lower densities may float on top of substances with higher densities.

5. What are some real-world applications of density of matter?

Density is used in a variety of industries and fields, including construction, engineering, and chemistry. It is used to determine the strength and stability of materials, design structures, and create products. For example, the density of a material can help determine its suitability for use in building structures or creating lightweight objects.

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