Question

at what average distances (in au) from the sun would you expect to find kirkwood gaps where the orbital period of asteroids are respectively three-sevenths, and two-sevenths, of the orbital period of jupiter? (hint: use kepler's third law.)

Answer 1

To find the average distance from the Sun for asteroids with specific orbital periods, we can use Kepler's third law. For a three-sevenths orbital period of Jupiter, the average distance is approximately 2.35 AU. For a two-sevenths orbital period of Jupiter, the average distance is approximately 1.68 AU.

Step-by-step explanation:

Kepler's third law states that the orbital period of a planet is proportional to the square root of the cube of its mean distance from the Sun.

We can use this law to calculate the average distance from the Sun (in AU) for asteroids with specific orbital periods.

To find the average distance for an asteroid with a three-sevenths orbital period of Jupiter's orbital period, we can set up the equation:

(3/7)^2 = (a/5.20)^3

Solving for a, we get:

a = 5.20 * (3/7)^(2/3)

= 2.35 AU

Similarly, for an asteroid with a two-sevenths orbital period of Jupiter's orbital period, we can set up the equation:

(2/7)^2 = (a/5.20)^3

Solving for a, we get:

a = 5.20 * (2/7)^(2/3)

= 1.68 AU