Line of sight and star density question.

[Illuminati]

This is blatant homework help that I don't know how to approach. Any hints would be appreciated.

Suppose you are in an infinitely large old universe in which the average density of stars is n = 10⁹ Mpc^-3 and the average stellar radius is equal to the sun's radius is R = 7*10⁸. How far, on average, could you see in any direction before your line of sight strikes a star?

 

[gneill]

Look up "mean free path".

 

[Ken G]

Also, be careful of the units here-- if the density is in terms of Mpc^-3, then you want the cross sectional area of the Sun in units of Mpc² to avoid having to convert units during your calculation. wolframalpha.com tells me that the answer for the Sun is 2 times 10^-38 Mpc². How can you combine that with the density to get a distance, which will be the mean free path you want? (It would require a pretty darn big universe to hit a star-- for one thing, the universe would need to be almost 10¹⁹ times older than it actually is, right?)

 

[Matterwave]

You can use dimensional analysis to get something out of this, and then see if it makes sense to you. 1/L^3 and L^2 can be combined how to get L?

This won't get you any constants or other unit-less things though, but maybe it will help you see the problem more clearly.

 

[pmacias]

I would approach this question by first understanding the concepts of line of sight and star density. Line of sight refers to the unobstructed path between an observer and an object, while star density refers to the number of stars per unit volume in a given region of space. In this scenario, we are given the average star density, n, in units of Mpc-3 (megaparsecs cubed), which is a measure of volume.

To determine the average distance that we could see in any direction before our line of sight strikes a star, we need to consider the volume of space that our line of sight covers. This can be calculated by taking the average stellar radius, R, and cubing it to get the volume of a single star. Then, we can multiply this volume by the average star density, n, to get the volume of space that is occupied by stars.

Next, we can calculate the distance that our line of sight would cover by taking the cube root of this volume. This distance represents the average distance that we could see in any direction before encountering a star. However, it is important to note that this is an average value and there may be regions of space with higher or lower star densities, which would affect the actual distance that we could see.

In conclusion, to answer the question of how far we could see before our line of sight strikes a star in this scenario, we would need to calculate the average volume of space occupied by stars and then take the cube root of this volume to get the average distance. This would give us an estimate of the maximum distance that we could see in any direction before encountering a star.