Difference between revisions of "Forest for the trees"
From Universe in Problems
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| − | === Problem 1 === | + | === Problem 1: the Olbers' paradox === |
If the Universe was infinitely old and infinitely extended, and stars could shine eternally, then in whatever direction you look the line of your sight should cross the surface of a star, and therefore all the sky should be as bright as the Sun's surface. This notion is known under the name of Olbers' paradox. Formulate the Olbers' paradox quantitatively [http://arxiv.org/abs/0706.1988 L. Anchordoqui, arXiv:0706.1988, physics.ed-ph]. | If the Universe was infinitely old and infinitely extended, and stars could shine eternally, then in whatever direction you look the line of your sight should cross the surface of a star, and therefore all the sky should be as bright as the Sun's surface. This notion is known under the name of Olbers' paradox. Formulate the Olbers' paradox quantitatively [http://arxiv.org/abs/0706.1988 L. Anchordoqui, arXiv:0706.1988, physics.ed-ph]. | ||
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| − | === Problem 2 === | + | === Problem 2: a down to earth setting === |
There are $n$ trees per hectare in a forest. Diameter of each one is $D$. Starting from what distance will we be unable to see the forest for the trees? How is this question connected to the Olbers' paradox$^*$? | There are $n$ trees per hectare in a forest. Diameter of each one is $D$. Starting from what distance will we be unable to see the forest for the trees? How is this question connected to the Olbers' paradox$^*$? | ||
$^*$ Ryden, Introduction to cosmology, ADDISON-Wesley. | $^*$ Ryden, Introduction to cosmology, ADDISON-Wesley. | ||
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| − | === Problem 3 === | + | === Problem 3: a Robin Hood setting === |
In a more romantic formulation this problem looks as following. Suppose that in the Sherwood Forest, the average radius of a tree is $30cm$ and average number of trees per unit area is $n=0.005m^{-2}$. If Robin Hood shoots an arrow in a random direction, how far, on average, will it travel before it strikes a tree? | In a more romantic formulation this problem looks as following. Suppose that in the Sherwood Forest, the average radius of a tree is $30cm$ and average number of trees per unit area is $n=0.005m^{-2}$. If Robin Hood shoots an arrow in a random direction, how far, on average, will it travel before it strikes a tree? | ||
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| − | === Problem 4 === | + | === Problem 4: the cosmological setting === |
The same problem in the cosmological formulation looks this way. Suppose you are in a infinitely large, infinitely old Universe in which the average density of stars is $n_{st}=10^11 Mpc^{-3}$ and the average stellar radius is equal to the Sun's radius: $R_{st}=R_{\bigodot}=7\cdot10^8m$. How far, on average, could you see in any direction before your line of sight strucks a star? | The same problem in the cosmological formulation looks this way. Suppose you are in a infinitely large, infinitely old Universe in which the average density of stars is $n_{st}=10^11 Mpc^{-3}$ and the average stellar radius is equal to the Sun's radius: $R_{st}=R_{\bigodot}=7\cdot10^8m$. How far, on average, could you see in any direction before your line of sight strucks a star? | ||
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| − | === Problem 5 === | + | === Problem 5: stars collisions === |
| − | Demonstrate, that stars in galaxies can be considered | + | Demonstrate, that stars in galaxies can be considered a collisionless medium. |
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Revision as of 14:50, 11 October 2012
Contents
Problem 1: the Olbers' paradox
If the Universe was infinitely old and infinitely extended, and stars could shine eternally, then in whatever direction you look the line of your sight should cross the surface of a star, and therefore all the sky should be as bright as the Sun's surface. This notion is known under the name of Olbers' paradox. Formulate the Olbers' paradox quantitatively L. Anchordoqui, arXiv:0706.1988, physics.ed-ph.
Problem 2: a down to earth setting
There are $n$ trees per hectare in a forest. Diameter of each one is $D$. Starting from what distance will we be unable to see the forest for the trees? How is this question connected to the Olbers' paradox$^*$?
$^*$ Ryden, Introduction to cosmology, ADDISON-Wesley.
Problem 3: a Robin Hood setting
In a more romantic formulation this problem looks as following. Suppose that in the Sherwood Forest, the average radius of a tree is $30cm$ and average number of trees per unit area is $n=0.005m^{-2}$. If Robin Hood shoots an arrow in a random direction, how far, on average, will it travel before it strikes a tree?
Problem 4: the cosmological setting
The same problem in the cosmological formulation looks this way. Suppose you are in a infinitely large, infinitely old Universe in which the average density of stars is $n_{st}=10^11 Mpc^{-3}$ and the average stellar radius is equal to the Sun's radius: $R_{st}=R_{\bigodot}=7\cdot10^8m$. How far, on average, could you see in any direction before your line of sight strucks a star?
Problem 5: stars collisions
Demonstrate, that stars in galaxies can be considered a collisionless medium.
