5.Go to Earth-Sun in the "to scale" mode. Click to show the masses of each object. At this point the Earths period should be 365 days (if it is not, just hit the reset button). Double the Sun’s mass. What is approximately the new period? Dont forget your units!
8. According to Newtons theory of gravity, if I double the mass of the Sun, by how much should the velocity of the Earth change? How much should the period change?. Does this agree with what you found in question 5? If not, why not?
Now imagine that instead of orbiting around an object you are orbiting inside of an object of uniform density (this is possible if you are orbting inside of a thin gas with no drag for example). We will assume the orbit is circular. Newton showed that the only mass that matter for your orbiting motion is the mass inside of the radius you are orbiting as the figure below shows.
where V is the volume which goes like the radius cube. The mass inside of a radius r increases as the volume increases. As I move the satellite further away from the center, there is more and more mass inside the orbit.
The figure below shows the measured speed of stars (in km/s) orbiting a neighbor galaxy as a function of distance from the center of that galaxy. Kpc stands for kilo parsec and it is an astronomical unit to measure distance. On the figure, we added the image of the galaxy. Amost all the visible matter ends at 4 kilo parsec. Can you explain the graph between 1 kpc and 4 kpc? What do you think is going on between 4 kpc and 6 kpc?
Between 4KPC and 6 KPc – Despite an increase in the radius increases the the velocity is increasing. The increase in velocity can be attributed to the fact that the masses of the of the bodies beween 4kpc and 6kpc are