Question

It is estimated that there are approximately 1 million asteroids that are larger than 1 km in size. If all asteroids orbited on the same plane at a radius of 2 AU from the Sun, and were equally spaced on this orbit, what would be the spacing between each of these large asteroids?

Answer 1

To calculate the spacing between 1 million evenly spaced asteroids on a 2 AU radius orbit, we first find the orbit's circumference using the formula C = 2πr. We then convert the AU to kilometers and divide the circumference by 1 million to determine the distance between each asteroid.

Step-by-step explanation:

The student is asking for the calculation of the spacing between asteroids if 1 million asteroids larger than 1 km in size were equally spaced along an orbit with a radius of 2 astronomical units (AU) from the Sun. To find the spacing, we first need to calculate the circumference of the orbit, which is done using the formula C = 2πr where π is the mathematical constant Pi (approximately 3.14159) and r is the radius in AU. Here, the radius is 2 AU, so the circumference C becomes 4π AU. As 1 AU is approximately 149.6 million kilometers, we convert this to kilometers to get a circumference in more familiar units. After calculating the circumference, we divide this value by 1 million to determine the spacing between each asteroid. Since the exact numbers are not provided in the question, this explanation outlines the process of calculating the spacing rather than providing a specific numerical answer.