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Solution to Exercise 9
In one hour, the asteroid moves 1.5 degrees. Thus the number of radians it moves is 1.5 deg / 57.3 deg = 0.026 radians. Remembering that the angle of something in radians is equal to the ratio of its diameter to its distance, we know that distance travelled in one hour X ------------------------------ = ---------------- = 0.026 distance to the asteroid 4,500,000 km Thus a distance X = 117,000 km has been travelled by the asteroid in one hour. Another way to solve this problem using trigonometry is to realize that 1.5 degrees is a very small angle; thus, you can approximate the ratio of transverse length to distance as the tangent of a right triangle with angle 1.5 degrees. In this case, tan(1.5 degrees) = 0.026 = X / 4,500,000 km and X = 117,000 km. Thus its transverse (i.e. horizontal) speed, with respect to our viewpoint on Earth, is 117,000 km / 3600 s = 32.5 km/s (your precision may vary). |