The Earth is 93.0 million miles 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?

Question

Quizplus · Accepted Answer

We can use the formula for centripetal acceleration:

a = v^2 / r

where v is the velocity of the Earth in its orbit and r is the distance between the Earth and the Sun.

The velocity of the Earth can be found by dividing the circumference of its orbit by the period of revolution:

v = 2πr / T

Substituting in the given values, we get:

v = 2π(93.0 × 10^6 miles) / (3.15 × 10^7 s)
v = 29.8 mi/s

Substituting this into the formula for acceleration, we get:

a = (29.8 mi/s)^2 / (93.0 × 10^6 miles)
a = 9.37 × 10^-17 mi/s^2

This is equivalent to 3.70 × 10^-16 mi/s^2 when rounded to two significant figures.

Therefore, the best choice is D, 3.70 × 10^-16 mi/s^2.

The Earth Is 93