The Earth is 93 million miles (mi)from the Sun and its period of revolution is 1 year = 3.15 × 10⁷ s.What is the acceleration of the Earth in its orbit about the Sun? A) 18.6 mi/s² B) 9.3 × 10−³ mi/s² C) 13.6 × 10−⁶ mi/s² D) 3.7 × 10−⁶ mi/s²

Question

Quizplus · Accepted Answer

The acceleration of the Earth in its orbit is given by:

a = (4π^2r) / T^2

where r is the distance between the Earth and the Sun, and T is the period of revolution.

Substituting the given values:

a = (4π^2 * 93,000,000) / (3.15 × 10^7)^2
  = 3.7 × 10^-16 mi/s^2

Converting to scientific notation with proper units:

a = 3.7 × 10^-16 mi/s^2
  = 3.7 × 10^-8 m/s^2
  = 3.7 × 10^-8 / 1.609 km/s^2  (converting miles to kilometers)

a = 2.3 × 10^-8 km/s^2

Therefore, the best choice is (D) 3.7 × 10^-16 mi/s^2.

The Earth Is 93 Million Miles (Mi)from the Sun and Its