Newton's Theory of Gravity: Calculating the Orbit of Our Solar System

[mcnealymt]

Homework Statement

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0*10^8 m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.

A)Assuming the orbit is circular, what is the period of the solar system's orbit? Give your answer in years.

B) Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?

c) The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?

D)Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?

Homework Equations

The Attempt at a Solution

A) I know the period by using the equation
v=(2pi * r)/ T
T= (2pi *r)/ v
My problem I can't even interpret the given information. I know that 25,000 light years has something to do with the radius. I have a feeling that I'm supposed to multiply 25,000 light years with 3.0 *10^8



For parts B-D I am completely lost...

 

[CWatters]

My problem I can't even interpret the given information. I know that 25,000 light years has something to do with the radius. I have a feeling that I'm supposed to multiply 25,000 light years with 3.0 *10^8

Almost.

Distance(m) = Velocity(m/s) * time(s)

Time = 25,000 years
Velocity = 3.0*10^8 m/s

You need to convert 25,000 years to seconds first

 

[CWatters]

More hints..

For A..

If you know the radius you can calculate the circumference of the orbit.
The velocity is stated so you can work out how long it takes to make one orbit.

For B..

If you know how long one orbit takes (from B) and you know how old the earth/solar system is you can work out how many orbits the solar system might have made in it's lifetime to date.

For C and D...

Centripetal force is provided by gravity. Whats the equation for the force of gravity between two bodies?

 

[mcnealymt]

Okay for part A) I found the radius and can use the equation T= (2pi*r)/v .

B) How does the age of the solar system help me? It just states an age and nothing else.

C) & D) The equation is g= (G*m1*m2)/r^2

However, what would be the mass of the galactic center in this equation?

 

[Bandersnatch]

B) How does the age of the solar system help me? It just states an age and nothing else.

For example, you know that the Earth's orbital speed is one orbit per year. How many orbits has it completed since it was formed 4,5 billion years ago?

Same here, only the speed is different.

C) & D) The equation is g= (G*m1*m2)/r^2

However, what would be the mass of the galactic center in this equation?

This is the equation for gravitational force, so you should label it F_g. g is the acceleration in a gravitational field.
In there, one mass is the mass of the orbiting body, the other one is that of the central body.

For circular motion, the force tugging on the orbiting body(the above) needs to be exactly equal to the value known as centripetal force.
Can you take it from here? Write the equation and see if you can get rid of any variables.