NASA’s Mysteries of the Universe: Dark Matter Janet Moore NASA Educator Ambassador Janet Moore NASA Educator Ambassador.

NASA’s Mysteries of the Universe:

Dark Matter

Janet MooreNASA Educator Ambassador

Merry-Go-Round

Merry-Go-Round

Solar System

Solar System

Solar System

Solar System

In Summary - Solar SystemOrbital speed

depends on force of gravity

Force of gravity depends on mass within the radius

Therefore, orbital speed depends on mass within the radius

What About Galaxies?

How would you expect stars to move around in a spiral galaxy?

What would you expect the mass distribution in a spiral galaxy to be?

The Activity - NGC 2742

You will be given:Rotation Curve

(velocity vs. radius)Luminosity Curve

(luminosity vs. radius)

Use the Data Chart to analyze the mass in the galaxy

G = 4.31 x 10-6

Sample Data ChartRadiu

sRot. Vel.

Grav. Mass

Lum. Lum. Mass

Lum/Grav

1 80 1.5 e9 3 e8 6 e8 0.4

3 100 6.9 e9 1 e9 2 e9 0.29

5 120 1.7 e10

2 e9 4 e9 0.24

8 140 3.6 e10

3.5 e9 7 e9 0.19

Evidence for Dark Matter

Light (visible matter) drops off as you go farther out in a galaxy

BUT . . . Velocities do not drop off

Result: Dark Matter mass is about 10x Luminous Matter mass

What is Dark Matter?Baryonic (Normal) Matter:

Low mass stars, brown dwarfs (likely), large planets, meteoroids, black holes, neutron stars, white dwarfs, hydrogen snowballs, clouds in halo.

Non-Baryonic (Exotic) Matter:Hot Dark Matter: fast-moving at time of

galaxy formation, eg massive neutrinosCold Dark Matter: slow-moving at times of

galaxy formation, eg WIMPs -- particle detector experiments looking for them

NASA’s Fermi Mission

Common Core Mathematical Practices

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in

repeated reasoning.

Mathematical modeling 1. Observing a phenomenon, delineating the problem

situation inherent in the phenomenon, and discerning the important factors that affect the problem.

2. Conjecturing the relationships among factors and interpreting them mathematically to obtain a model for the phenomenon.

3. Applying appropriate mathematical analysis to the model. 4. Obtaining results and reinterpreting them in the context

of the phenomenon under study and drawing conclusions.

Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. (pp. 2-3). Reston, VA: National Council of Teachers of Mathematics.

Questions?

Janet Moore

[email protected]

epo.sonoma.edu