RW 5 Name___________________Read 2b.5 – 2b.8About this assignmentEncounter with an asteroid.This is a large problem. Work it on paper before attempting to turn in your results and explanations here. You must turn in your diagram for part (a) on paper.In June 1997 the NEAR spacecraft, on its way to photograph the asteroid Eros, passed within 1200 km of asteroid Mathilde at a speed of 10 km/s relative to the asteroid (Figure2.34). From photos transmitted by the 805 kg spacecraft, Mathilde's size was known to be about 70 km by 50 km by 50 km. It is presumably made of rock. Rocks on Earth have a density of about 3000 kg/m3 (3 grams/cm3).(a) Make a diagram to show qualitatively the effect on the spacecraft of this encounter with Mathilde.Show the trajectory starting when the spacecraft is approaching Mathilde from far away, and continuing to when it is moving away from the asteroid and is again far away. This diagram is important for visualizing what happens. You will turn in the diagram on paper in class.(b) Make a very rough estimate of the magnitude of the change in momentum of the spacecraft that would result from encountering Mathilde.|p| ___________ kg·m/sExplain in detail how you made your estimate.(c) Using your result from part (b), make a rough estimate of how far off course the spacecraft would be, one day after the encounter. (You will be given credit for this part if it is consistent with your answer to part b, even if the answer to part b is incorrect.)______________ m(d) From actual observations of the location of the spacecraft one day after encountering Mathilde, scientists concluded that Mathilde is a loose arrangement of rocks, with lots of empty space inside. What was it about the observations that must have led them to this conclusion?Experimental background: The position was tracked by very accurate measurements of the time that it takes for a radio signal to go from Earth to the spacecraft followed immediately by a radio response from the spacecraft being sent back to Earth. Radio signals, like light, travel at a speed of 3×108 m/s, so the time measurements had to be accurate to a few nanoseconds (1 ns = 10-9
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