A graph is plotted between the logarithm of the time period of revolution ( T ) on the y-axis and the logarithm of the semi-major axis ( r ) on the x-axis for various planets orbiting the Sun. The slope of the resulting straight line will be

Step-by-step solution

According to Kepler's third law of planetary motion, the square of the time period of revolution ( T ) is directly proportional to the cube of the semi-major axis ( r ) of the orbit. T ^2 r ^3 T ^2 = K r ^3 Taking logarithm on both sides, we get: 2 T = 3 r + K T = 3 2 r + 1 2 K Comparing this with the equation of a straight line, y = mx + c , where y = T and x = r , the slope m is given by: m = 3 2 Answer: 3 2