Astrophysics distribution question

In summary, by using the formula for centripetal force and the universal law of gravitation, we can estimate the number of stars in the Milky Way galaxy. Assuming a uniform distribution of stars and using the mass and distance of our star, we find that there are approximately 0.39 stars in the galaxy. The value of G is 6.67x10^-11 Nm^2/kg^2.
  • #1
lando45
84
0
"A star, with mass 5.40*10^30 kg, revolves about the center of the Milky Way galaxy, which is 3.93*10^20 m away, once every 3.41*10^8 years. Assuming that each of the stars in the galaxy has a mass equal to that of our star, that the stars are distributed uniformly in a sphere about the galactic center, and that our star is essentially at the edge of that sphere, estimate roughly the number of stars in the galaxy."

I don't really understand how I am supposed to answer this question. Using simple mathematics I can calculate the distance traveled of this star, and the speed with which it travels, but I do not know what else I need to do. I don't see where the mass comes into it, is volume and/or density relevant? I suspect this might be something to do with the Maxwell-Boltzmann distribution, am I in the right direction? Thanks.
 
Physics news on Phys.org
  • #2
lando45 said:
"A star, with mass 5.40*10^30 kg, revolves about the center of the Milky Way galaxy, which is 3.93*10^20 m away, once every 3.41*10^8 years. Assuming that each of the stars in the galaxy has a mass equal to that of our star, that the stars are distributed uniformly in a sphere about the galactic center, and that our star is essentially at the edge of that sphere, estimate roughly the number of stars in the galaxy."

I don't really understand how I am supposed to answer this question. Using simple mathematics I can calculate the distance traveled of this star, and the speed with which it travels, but I do not know what else I need to do. I don't see where the mass comes into it, is volume and/or density relevant? I suspect this might be something to do with the Maxwell-Boltzmann distribution, am I in the right direction? Thanks.
No, it has nothing to do with the MB distribution.

The idea is this: the centripetal force is provided by the force of gravity, right? So [itex] {m v^2 \over r } = {G m M \over r^2}[/itex], right? Now, what is the meaning of m and M? m is the mass of the star and it cancels out. M is the mass of *all the stars within a radius r form the center of the galaxy*. Therefore, if you divide this mass by the mass of a single star, you get the total number of stars (assuming they all have the same mass) *within the radius r* (that is all the stars that are closer to the center of the galaxy than the star you are considering). This is why they had to add that the star is at the edge so that you may say that the number you get is the total number of stars in that galaxy. Now that you know the toatl number of star, it`s easy to calculate their density (assuming it's uniform), right?

Patrick
 
  • #3
Right, that does makes sense, but I just tried, and got an answer which is clearly wrong. Here's what I did:

(m*v^2)/r = (G*m*M)/r^2
m = 5.40*10^30 kg
G = 9.81 ms^-2
r = 3.93*10^20 m
v = d/t
v = (2*pi*r)/t
v = (2*pi*3.93*10^20)/(3.41*10^8*365.25*24*60*60)
v = (2.469*10^21)/(1.076*10^16)
v = 229,460 ms^-1
(v^2)/r = (G*M)/r^2
M = (v^2*r^2)/(G*r)
M = (v^2*r)/G
M = (229,460^2*3.93*10^20)/9.81
M = 2.109*10^30 kg
Number of stars = M/m = 2.109*10^30/5.40*10^30
Number of stars = 0.39

This clearly can't be right? The areas I may have possibly gone wrong in are a) my value for G; should it be 9.81? or b) my manipulation of the formula to have M as the subject. HELP!
 
  • #4
lando45 said:
Right, that does makes sense, but I just tried, and got an answer which is clearly wrong. Here's what I did:

(m*v^2)/r = (G*m*M)/r^2
m = 5.40*10^30 kg
G = 9.81 ms^-2
r = 3.93*10^20 m
v = d/t
v = (2*pi*r)/t
v = (2*pi*3.93*10^20)/(3.41*10^8*365.25*24*60*60)
v = (2.469*10^21)/(1.076*10^16)
v = 229,460 ms^-1
(v^2)/r = (G*M)/r^2
M = (v^2*r^2)/(G*r)
M = (v^2*r)/G
M = (229,460^2*3.93*10^20)/9.81
M = 2.109*10^30 kg
Number of stars = M/m = 2.109*10^30/5.40*10^30
Number of stars = 0.39

This clearly can't be right? The areas I may have possibly gone wrong in are a) my value for G; should it be 9.81? or b) my manipulation of the formula to have M as the subject. HELP!
No, G is the constant appearing in the universal of gravitation, 6.67x10^-11 Nm^2/kg^2. The rest seems ok to me (notice that you don't even need the mass of the star to find M, it's only when you find the number of stars that m is needed)
 
  • #5
Ah that yielded the correct answer. Many thanks for your help buddy.
 

1. What is an astrophysics distribution?

An astrophysics distribution refers to the way in which matter and energy are distributed throughout the universe. This includes the distribution of galaxies, stars, planets, and other celestial bodies, as well as the distribution of dark matter and dark energy.

2. How is the distribution of matter and energy in the universe measured?

The distribution of matter and energy in the universe is measured through various methods, including observations with telescopes, mathematical models, and simulations. Scientists also use data from cosmic background radiation and the large-scale structure of the universe to study its distribution.

3. What is the significance of studying astrophysics distribution?

Studying astrophysics distribution helps us understand the fundamental laws of the universe and how it has evolved over time. It also provides insights into the formation and evolution of galaxies, stars, and planetary systems. Furthermore, studying distribution can help us better understand the mysterious phenomena of dark matter and dark energy.

4. How does the distribution of matter and energy affect the universe?

The distribution of matter and energy has a significant impact on the universe. It determines the structure and behavior of galaxies, the formation of stars and planets, and the expansion of the universe. It also plays a crucial role in shaping the large-scale structure of the universe and can influence the occurrence of cosmic events such as supernovae and black holes.

5. What are some current research topics related to astrophysics distribution?

Some current research topics related to astrophysics distribution include studying the distribution of dark matter and dark energy, understanding the formation and evolution of galaxies and galaxy clusters, and investigating the distribution of matter and energy in the early universe. Scientists are also exploring the effects of cosmic expansion on the distribution of matter and energy and studying the distribution of exoplanetary systems in our galaxy.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
991
Replies
6
Views
949
  • Astronomy and Astrophysics
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
894
Replies
22
Views
2K
  • Astronomy and Astrophysics
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
911
Back
Top