Question

Find the speed of the Earth in its orbit about the Sun, using the distance 1.0 AU from Sun to Earth. Give the answer in km/s to two significant figures.

Answer 1

T = time period of earth for one complete orbit = 365 days = 365 x 24 hours = 365 x 24 x 3600 sec = 3.15 x 10⁷ sec

angular speed of earth about the sun is given as

w = 2/T

r = radius of orbit about sun = 1 Au = 1.5 x 10¹¹ m

v = speed of earth in the orbit

Speed of earth is hence given as

v = r w

v = (1.5 x 10¹¹) (2/T )

v = (1.5 x 10¹¹) (2(3.14)/(3.15 x 10⁷) )

v = 3.0 x 10⁴ m/s

v = 30 km/s