If each galaxy contains 1 hundred billion stars, and there are 1 hundred billion galaxies, and 89% of all stars are low mass like the Sun, and 1 in 5 low mass stars like the Sun have planets like Earth in the habitable zone, what is the number of planets that exist in the Universe that are in the habitable zones of their low mass stars? (hint: use your favorite, dimensional analysis! try this on paper!) Start with 1 Universe, then convert to galaxies and so on. (For 89% use this conversion factor: 89 low mass stars /100 stars)*1 point4.88 x 10^28 planets2.99 x 10^18 planets8.93 x 10^15 planets1.78 x 10^21 planets
Question
If each galaxy contains 1 hundred billion stars, and there are 1 hundred billion galaxies, and 89% of all stars are low mass like the Sun, and 1 in 5 low mass stars like the Sun have planets like Earth in the habitable zone, what is the number of planets that exist in the Universe that are in the habitable zones of their low mass stars? (hint: use your favorite, dimensional analysis! try this on paper!) Start with 1 Universe, then convert to galaxies and so on. (For 89% use this conversion factor: 89 low mass stars /100 stars)*1 point4.88 x 10^28 planets2.99 x 10^18 planets8.93 x 10^15 planets1.78 x 10^21 planets
Solution
Sure, let's break it down step by step.
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Start with the total number of stars in the Universe:
- Each galaxy contains 1 hundred billion stars.
- There are 1 hundred billion galaxies.
- Total number of stars = (1 hundred billion stars/galaxy) * (1 hundred billion galaxies)
- Total number of stars = (10^11 stars/galaxy) * (10^11 galaxies)
- Total number of stars = 10^22 stars
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Calculate the number of low mass stars:
- 89% of all stars are low mass stars.
- Number of low mass stars = 0.89 * Total number of stars
- Number of low mass stars = 0.89 * 10^22
- Number of low mass stars = 8.9 * 10^21
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Determine the number of low mass stars with planets in the habitable zone:
- 1 in 5 low mass stars have planets in the habitable zone.
- Number of low mass stars with habitable zone planets = (1/5) * Number of low mass stars
- Number of low mass stars with habitable zone planets = 0.2 * 8.9 * 10^21
- Number of low mass stars with habitable zone planets = 1.78 * 10^21
So, the number of planets that exist in the Universe that are in the habitable zones of their low mass stars is 1.78 x 10^21.
The correct answer is: 1.78 x 10^21 planets
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