17. In Einstein's theory of gravity, light passing a star of mass M, at a distance...

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17. In Einstein's theory of gravity, light passing a star of mass M, at a distance R from the centre of the star, is bent by an angle (measured in radians, 27 radians = 360°) as shown in the diagram. (a) Assume that depends on the gravitational constant G and also depends on the mass of the star M, the distance R and the speed of light c = 3 × 108 ms ¹, as 0=XGM° R³c7, where A is an undetermined dimensionless constant. By considering the dimensions of these quantities determine a, 3 and y. (b) In SI units the numerical value of G is 6.67 x 10-11 Neglecting any spatial extent to the star, and taking A = 1 and M = 2 × 10³0 kg, determine the distance R such that light is bent so much that it falls directly into the star. M O R Ө [4] [3] 17. In Einstein's theory of gravity, light passing a star of mass M, at a distance R from the centre of the star, is bent by an angle (measured in radians, 27 radians = 360°) as shown in the diagram. (a) Assume that depends on the gravitational constant G and also depends on the mass of the star M, the distance R and the speed of light c = 3 × 108 ms ¹, as 0=XGM° R³c7, where A is an undetermined dimensionless constant. By considering the dimensions of these quantities determine a, 3 and y. (b) In SI units the numerical value of G is 6.67 x 10-11 Neglecting any spatial extent to the star, and taking A = 1 and M = 2 × 10³0 kg, determine the distance R such that light is bent so much that it falls directly into the star. M O R Ө [4] [3]

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