Question

The radius of the earth’s orbit is r = 1.5 × 1011 m and its orbital period is T = 365.3 days. What is the radial acceleration (in m/s2) of the earth toward the sun, assuming a circular orbit?

A. 5.91 × 10−3 m/s2
B. 3.23 × 10−3 m/s2
C. 7.23 × 10−4 m/s2
D. 5.91 × 10−2 m/s2

Answer 1

The radial acceleration of a body a distance R from the center of a circular path and with period T has magnitude a such that

a = 4 π ² R / T ²

The given period is

T = 365.3 days ≈ 3.156 x 10⁷ s

(i.e. multiply the number of days by 24 hours/day and 3600 seconds/hour)

So the Earth's radial acceleration is

a = 4 π ² (1.5 x 10¹¹ m) / (3.156 x 10⁷ s)²

a ≈ 0.0059 m/s²