Question

Kepler's Law, which states that the square of the time, T (measured in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, d (measured in billions of kilometers), that the planet is from the Sun. 19 a. It takes Saturn approximately 30 Earth years to orbit the Sun with a mean distance of 1.4 billion kilometers. Use this information to find the equation relating T and d with the numerical value of k (rounded to 2 decimal places).

please answer and show work for all parts of equation

Answer 1

19a → From the keplers third law, the square of the period of a comet is directly proportional to the cube of its radius of the orbit. p² o aš p2 = ka terbang (307) (1.42) (30) T 2 = (1.4) 72 x 328 72 = (3:28x102) ►Two decimal places 3 19(1) ► Now, pa = ka? = (3.28x10)a? =(3.28x10^)(2.5) (3.28x10^)(2.5)* = 71.589 years 71.6 years P = = EX = 19(11) ► Now, 3 = 2 15 A= (3.5) (3.2810*) = 0.334 billion kilometers *