試題詳解

19. There is an interesting experiment that enables us to estimate the mass density of the sun. Consider (see Figure 5) an experimental setup that can get an image of the sun through a pinhole. The distance between the pinhole and the screen is d, and the diameter of the image is D. Because light propagates in a straight line (neglect geometrical distortions), you can obtain the angle θin terms of d and D. Therefore, the relationship between R and r can be exhibited, where R is the radius of the sun and r is the distance between the earth and the sun. It is known that the earth orbits the sun by the period days. Assume that the earth makes a circular orbit around the sun, and the sun is a perfect sphere. From these hints, the mass density of the sun p is given by
  
(A)
(B)
(C)
(D) , where G= is the gravitational constant.