# What is the Calculation for the Number of Stars in the Solar Neighborhood?

• Fox
In summary, The "solar neighborhood" is defined as all the stars within a radius of 100 parsecs of the sun. The region near the sun can be represented as a disk with a constant star density in the central xy plane, but varying as D = D(o) * exp (-|z|/B) normal to the central plane. Using cartesian coordinates, the number of stars in the solar neighborhood can be calculated by integrating D(o) * exp (-|z|/B) over the y and z directions. The integral is similar to calculating the volume of a cylinder with radius 100 parsecs and height B. It may be helpful to refer to the provided diagram.
Fox
I'll admit, I'm fried. If I can just solve this one problem before the end of the night, I'll be golden though. All help is appreciated... the wording is a bit tricky, which is killing me.

The "solar neighborhood" can be defined as all the stars of the galaxy within a radius of 100 parsecs (pc.) of the sun. The region of the galaxy near the sun can be represented by a disk, where the density of the stars is constant in the central xy plane of the disk but varies as:

D = D(o) * exp (-|z|/B)

normal to the central plane of the disk. D(o) = 1/9 pc^-3 and B = 500 pc is the effective half thickness of the disk. Use cartesian coordinates to calculate the number of stars in the solar neighborhood. Hint: Do the y integral first and the z intergral last.

If someone could even give me any sort of hint on how to set this things up (ex. The intergration) it would help greatly. This is the last problem of the year... and I'm fried... and can barely think.

Last edited:
The integral in the y direction is constant, in the z direction it is variable though, this is obvious in the function. You are just integrating a sphere with radius 100 parsecs, the integrand is the above function.

edit: cylinder, not sphere.

Last edited:
Have to admit, I don't get it.

Do I just intergrate D(o)*e^(|z|/B) dy dx dz ?

Here's the drawing he gave us to go with it. It's a bit blurry, but maybe it'll help more :)

http://i3.photobucket.com/albums/y89/tcnjfox/IMG_0327.jpg

thanks guys :)

Last edited by a moderator:
can anyone help clarify this for me? :)

## 1. What is the last problem of the year?

The last problem of the year is the final question or challenge given to students or participants at the end of a school year or competition. It is meant to test their knowledge and skills and is often considered the most difficult problem of the year.

## 2. How is the last problem of the year chosen?

The last problem of the year is usually chosen by teachers or coordinators based on its level of difficulty and relevance to the subject or competition. It may also be chosen by a panel of judges or experts in the field.

## 3. Is the last problem of the year different every year?

Yes, the last problem of the year is usually different every year to challenge students and avoid repetition. However, it may be based on similar concepts or themes as previous years.

## 4. Can students work together to solve the last problem of the year?

It depends on the rules set by the teacher or competition organizers. Some may allow collaboration while others may require individual work. It is important to follow the guidelines to ensure fairness.

## 5. How important is the last problem of the year?

The last problem of the year is often considered important as it is a culmination of what students have learned throughout the year. It also serves as a final assessment of their knowledge and skills and may have an impact on their overall grade or standing in the competition.

### Similar threads

• Introductory Physics Homework Help
Replies
6
Views
2K
• Cosmology
Replies
7
Views
1K
• Astronomy and Astrophysics
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
4K
• Introductory Physics Homework Help
Replies
4
Views
11K
• Special and General Relativity
Replies
5
Views
1K
• Astronomy and Astrophysics
Replies
1
Views
1K
• Sci-Fi Writing and World Building
Replies
31
Views
2K
• Advanced Physics Homework Help
Replies
1
Views
927
• Sci-Fi Writing and World Building
Replies
21
Views
1K