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The acceleration of an object moving in the gravitational field of the Earth is a = ─ GMEr/r3 where r is the position vector directed from the center of the Earth toward the object. Choosing the origin at the center of the Earth and assuming that the small object is moving in the xy plane, we find that the rectangular (Cartesian) components of its acceleration are Ax = − GMEx / (x2 +y2) 3/2 ay = − GMEy/ (x2 + y2)3/2 Use a computer to set up and carry out a numerical prediction of the motion of the object, according to Euler’s method. Assume the initial position of the object is x = 0 and y = 2RE, where RE is the radius of the Earth. Give the object an initial velocity of 5 000 m/s in the x direction. The time increment should be made as small as practical. Try 5 s. Plot the x and y coordinates of the object as time goes on. Does the object hit the Earth? Vary the initial velocity until you find a circular orbit. |
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