You are on a space mission to land on various asteroids in the solar system. Aft
ID: 801946 • Letter: Y
Question
You are on a space mission to land on various asteroids in the solar system. After many long years in cramped quarters and some "misunderstandings" with your crewmates. you've developed a nagging suspicion that they are planning to leave you behind on the next asteroid.^1 You've decided that you're only going out there again if you can jump off the asteroid under your own power to get back to your spaceship before it can leave without you. Can you do it? Let's find out... (a) Estimate the velocity you achieve when you jump straight up. (b) Now estimate the radius of the largest asteroid you could escape from by jumping. (You will need to make an assumption about the mean density of asteroids, which are made of rock and ice; be sure to explain your reasoning.)Explanation / Answer
A) By consideration of Newton's Law of Gravitation and the conservation of total energy and momentum, it may be possible to leave the field of asteroid by my own energy. Since the asteroid has significantly weak gravity field as compare to our earth or any large planet; thus as considerable jump may lead us to create an escape velocity for that particular asteroid. Further, at the same time it become important to estimate the optimum thrust so that one can be able to leave its field as well as can maintain the balance velocity after leaving to the space.
b) The mean density of the asteroid has an emperical relation with the estimated radius with some RMS values.Since, this particular asteroid is made up of ice and rocky materials ; its mean density may be minimal in value as compared to the material/ density of the terresterial planet. thus, if it was being the part of the rotational frame of inertia ( in its evolutiion period) then, the the radius can be higher and gravity feel will be lesser as expected.
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