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Kysyvä_1 kirjoitti:

Laitoin saman kysymyksen Hollantilaisille, jotka ovat tunnetusti välkkyjä astronomiassa, ja seuraavassa vastaus:

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Kysymys:

Let's say my weight is 70 kg and I can jump 1 meter high on Earth. How large is the planet from which I can jump out? (I am assuming that if the planet is small enough, I can push it away from me with my legs)

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Vastaus:

If you can jump 1 meter high on Earth, then your initial upward speed is about 4.5 m/s. I do not think that you'll be able to reach a very much greater initial speed if you jump up from another planet, even if it is a much smaller one, because you just cannot move your legs much faster.

So, your question is really how large a planet can be before its escape speed (the initial speed you need to escape from the planet's gravity) gets greater than about 5 m/s.

The escape speed of a round planet in meters per second is equal to 0.75 times the square root of the average mass density compared to that of water, times the radius measured in kilometers. For example, the average mass density of the Earth is about 5.5 times that of water, and the radius of the Earth is about 6400 km, so the escape speed from the Earth is about 0.75 times the square root of 5.5, times 6400 = about
11,000 m/s or 11 km/s.

For a planet with a mass density of twice that of water (which seems reasonable for a small planet), this means that the escape speed measured in meters per second is about equal to the radius of the planet measured in kilometers. For the escape speed to be not more than 5 m/s,
the radius of such a planet must be not more than about 5 km.

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Elikkä laskenta on periaatteessa sama, mutta hänen mielestään pienen planeetan tiheyden tulee olla kaksi kertaa suurempi kuin veden.

Linkki Hollantilaisten sivuille

http://www.astro.uu.nl/~strous/AA/en/index.html

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