Question

At certain distances from the Sun, asteroids in the main asteroid belt are in an orbital resonance with Jupiter, creating gaps in the belt called Kirkwood gaps. Jupiter orbits the Sun with a period of 11.9 years.

Which of the following is not a period of an asteroid that is in an orbital resonance with Jupiter?

Answer 1

3.97

Explanation: i got it right on the hw

Answer 2

The answer is 3.40

Step-by-step explanation:

To determine which of the given periods is not in an orbital resonance with Jupiter, we need to calculate the resonant periods using the formula:

Resonant Period = (jupiter_period * asteroid_period) / |2 * jupiter_period - asteroid_period|

Let's calculate the resonant periods for the given options:

a) Resonant Period = (11.9 * 4.38) / |2 * 11.9 - 4.38| ≈ 47.082 / 19.44 ≈ 2.423

b) Resonant Period = (11.9 * 5.95) / |2 * 11.9 - 5.95| ≈ 70.805 / 5.95 ≈ 11.905

c) Resonant Period = (11.9 * 3.97) / |2 * 11.9 - 3.97| ≈ 47.083 / 19.86 ≈ 2.371

d) Resonant Period = (11.9 * 3.40) / |2 * 11.9 - 3.40| ≈ 40.46 / 20.8 ≈ 1.947

Comparing these results to the given periods:

a) 4.38 - In an orbital resonance with Jupiter

b) 5.95 - In an orbital resonance with Jupiter

c) 3.97 - In an orbital resonance with Jupiter

d) 3.40 - Not in an orbital resonance with Jupiter

Therefore, the answer is 3.40