Question

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).

A. 2.26 × 10²¹ m
B. 2.68 × 10²¹ m
C. 3.04 × 10²¹ m
D. 3.42 × 10²¹ m

Answer 1

Using the formula for the circumference of a circle, we calculated Earth's orbital circumference and multiplied by its age to find the total distance traveled. The calculation resulted in a total distance of about 3.77 × 10²± meters, which isn't exactly any of the given options.

Step-by-step explanation:

To compute the total distance the Earth has traveled in its orbit around the Sun, we can calculate the circumference of its orbit and multiply that by the number of years it has orbited. Since the question provides the Earth's orbital radius (1.5 × 10¹¹ m) and its age (about 4 × 10¹ years), we can use these values in our calculation.

The circumference, C, of Earth's orbit can be found using the formula C = 2πr, where r is the orbital radius. Plugging in the given radius, we get:

C = 2 × π × (1.5 × 10¹¹ m)

C ≈ 9.42 × 10¹¹ m

Now, we need to multiply the circumference by the number of orbits, which equals the number of years Earth has existed. So the total distance (D) traveled is:

D = C × number of years

D = (9.42 × 10¹¹ m) × (4 × 10¹ years)

D ≈ 3.77 × 10¹²± m

Looking at the options provided in the question, none of them match the calculated value exactly. Hence, there might be a mistake in the question or the options given. However, our calculated value aligns closely with option D, which is 3.42 × 10²± m, but our calculated answer is slightly higher.