Question

Analysis:

1. Consider your galaxy rotation curves. Describe how rotational velocity changes as a function of distance from galaxy center. Do all the galaxies show similar behavior?
2. Now compare the galaxy rotation curves to the curve you plotted for the solar system planets. How do they differ?
3. We know that most of the mass (>99%) of the solar system is in the Sun. Is this consistent with the masses you calculated in the first table, and the solar system rotation curve? Explain your answer.

4. What pattern do you notice about the masses calculated in the galaxy tables? How does this pattern differ from that of the solar system table?

5. Explain how your results imply the existence of dark matter in the halos of galaxy? (You may need to do additional research to make this connection.)

Answer 1

from above curve, we can see that near the centre the speed of rotation increases rapidly with distance. it increases to a certain value then becomes almost constant.

We can also see that stars which are near to the centre of the Galaxy Orbit the centre with same speed as compared to the stars which are far from the centre.

Almost all the galaxies shows similar behaviour but a very few of them show keplerian decline.

the above curve shows how the speed of rotation changes with respect to to distance from the centre.

as we can see that there is a whose difference between both of the curves.

speed of rotation of Galaxy increases to a certain point and then becomes almost constant while the orbital velocity of planets in a solar system decreases with increasing value of semi major axis.

Sun contains 99% mass of the solar system, there is an inconsistancy here which can be seen from the curve below.

The curve shows that at large distances the visible mass differs from the mass which is predicted from rotation curve .This can be explained by the concept of dark matter, which i have explained below.

From above data

We know that normal metter does not have sufficient gravitational force that can Bound the stars which are far away from the center of the Galaxy and orbiting with a very high speed. So we can conclude that The gravity of normal matter is not strong enough to hold stars together to form galaxies and complex structures of the existing universe.
Stars will scatter randomly in the space rather than forming galaxies.
So there has to be something that interacts with gravity but we can not see it because it doesn't interact with light and normal matter directly. Though it has gravity.

We call this thing dark matter. Dark matter does not affect the velocity of planets orbiting around the sun because it is distributed uniformly in the space. So for small distances we cannot see it's effect clearly.