 # 1. Escape velocity. Starting from the sun and planet preset, make ...

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1. Escape velocity. Starting from the sun and planet preset, make the following changes to the parameters: Mass Position Velocity X y X y Body 1 200 Body 2 0.1 142 119 In class, you determined what the simulator "thinks" the value of the universal gravitation constant G is. Write that value here. G = 10000 Your challenge now is to find the "escape velocity" for the planet. If the planet travels with an initial speed equal to the "escape velocity," then it will have enough initial kinetic energy to escape the sun and never come back, but without having any extra kinetic energy at all when it is "done escaping." Assuming that the planet is moving with an initial speed equal to the "escape velocity": a. In the limit that the final instant is an infinite time after the initial instant (or, more practically, a very long time after the initial instant): i. Is the kinetic energy of the planet positive, negative, or zero? Explain. ii. Is the gravitational energy of the planet-sun system positive, negative, or zero? (The answer is an example of truth by consensus - rather than appeal to the formula, which is the result of consensus, you should briefly discuss instead why the consensus makes sense.) iii. Is the total mechanical (kinetic plus gravitational) energy of the planet-sun system positive, negative, or zero? Explain. b. At the initial instant: i. Is the kinetic energy of the planet positive, negative, or zero? Explain. ii. Is the total mechanical (kinetic plus gravitational) energy of the planet-sun system positive, negative, or zero? Explain. iii. Is the gravitational energy of the planet-sun system positive, negative, or zero? Explain. c. Describe an advantage to thinking about question b.iii after question b.ii rather than before. d. Write an equation that stems from the logic of parts a and b, solve it algebraically, and then substitute in numerical values to determine the escape velocity. e. Check your prediction using the simulation. Did it work? How do you know? f. Change the direction of the initial velocity to be at a right angle to what it was previously. Does this work too - does the planet escape? Explain why your observation makes sense, in terms of energy. g. Describe what happens in the simulation if you underestimate the escape velocity, and the simulation is allowed to run for a very long time. h. Describe what happens in the simulation if you overestimate the escape velocity, and the simulation is allowed to run for a very long time.

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