1. Gravity Lensing and Dark Matter
Emily Low
Emily Rodrigo
Sophia Lahey

2. Our Goal
Our goal was to use gravity lensing to find the mass of a galaxy, then estimate the expected mass and subtract the two to find dark matter.

3. Finding the Angle
To start out we needed to find the angle between the galaxy and the lensed galaxy ring around it. We did this by counting pixels between the ring and the center of the galaxy.
This gave us Einstein radius.
V filter
R filter

4. We found that the mass of LRG 3-757 is
Einstein Formula
Now we could solve the formula shown above for M to get the mass. G was a constant for gravity, c was the speed of light, and we found the d numbers using an equation.
We found that the mass of LRG is
7.5(10^12)
Now we needed to find the expected matter the galaxy should have.

5. The Black Hole
The first thing we decided to find was the mass of the black hole in the center of LRG But after some research we discovered that the black hole was only .01% of the galaxies mass and we didn't even need to include it in our calculations.

6. Gas and Dust
To find the amount of gas and dust in our galaxy we averaged the percentage of gas and dust in elliptical (01%) and spiral (4%) and got 2.005%. We did the math and discovered that LRG has 1.5(10^11) solar masses of gas and dust.

7. Stars
We found that our galaxy has around 6 trillion stars. Since an average star is one tenth of are suns mass we divided 6 trillion by ten to get 6(10^11) solar masses.

8. This is the expected result.
Our Result
The total mass in LRG is 7.5(10^12) solar masses. The total expected or visible mass is 7.5(10^11). This is one tenth of the total mass.
The total dark matter in LRG is
6.75(10^12) solar masses
90% of the galaxy
This is the expected result.