(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We have been asked to calculate the density of dark matter in the solar system. ive used the following equation:

2. Relevant equations

rho= 3v^2/4gPir^2

3. The attempt at a solution

V = 2.2*10^5 speed of solar system orbit around the galaxy

G = 6.67*10^-11 gravitational constant

PI 3.145

R = 2.5*10^20 the radius of the suns distance to the galactic centre in meters

SO 3*2.2*10^5= 1.45*10^11

Divided by

4*6.67*10^-11*3,14*8.95*10^41

=2.77*10^-21

Wen my lecturer gave us this equation he didnt specify what units the answer should be.

Assuming its kg/m^3

I then tried to work out the mass of the solar system , via assuming

mass = density*volume.

I assumed i should get a number about 5 times the mass of the sun as dark matter normally outweighs baryonic matter by about this ratio.

Instead

I got Density is equal to mass over volume

P = m/v

We know know

P = 2.77*10^21 kg/m^3

The volume of a sphere is 4/3Pir^3

We need to know the radius of the solar system, this is not an easy to number to determine as there is no definite edge to the soalr system. However 100 Au is usually quoted.

We have to covert this to meters. 1 Au is 1.49*10^11

100 times this is 1.49*10^13

4/3*Pi*(1.49*10^13^3)

= 1.4*10^40 m^3

No we can determine the mass of the solar system

Reaaranging the equation

P=m/v to solve for for m

We have

M= p*v

2.77*10^-212kg m^3*1.4*10^40

=3.8*10^19

which is less than the mass of the sun!!! the mass of the sun is 2*10^30kg

Where have i gone wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Dark matter density calculation

**Physics Forums | Science Articles, Homework Help, Discussion**