Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun).

Answer 1

Circumference = pi*2r = 3.14 * 3*10^11 = 9.42*10^11 m.

d = 9.42*10^11m/rev * 1rev/6.28rad * 7.29*10^-5rad/s * 3600s/h * 24h/da * 365da/yr. * 4*10^9yrs = 1.379*10^24 m.

Answer 2

Find circumference:
pi2r = 3.14*2*(1.5x10^11)
= 9.42x10^11
Now distance
d = (4x10^9) (9.42x10^11) = 37.7x10^20m
Distance traveled = 37.7x10^20m