Question

The arbitrary division where short-period comets end and

long-period comets begin is 200 years.
Using Kepler's third law for bodies orbiting the Sun, calculate the
semimajor axes for the orbits of a The arbitrary division where short period comets end and long-period comets begin is 200 years. Using Kepler's third law for bodies orbiting the Sun, calculate the semimajor axes for the orbits of a s

Answer 1

To find the semimajor axis for the orbit of a comet with a 200-year period, square the period (200 years) to get 40,000, then take the cubic root of this number, resulting in approximately 34.19 AU, which indicates the average distance from the Sun for long-period comets.

Step-by-step explanation:

The division between short-period and long-period comets is set at 200 years. To calculate the semimajor axes of these comets' orbits using Kepler's third law, we can start by considering the law itself, which states that a planet's orbital period squared (P ²) is proportional to the semimajor axis of its orbit cubed (a³). The given period for these comets is 200 years, so we can use this value to find the semimajor axis.

To calculate the semimajor axis (a), we follow the steps given by Kepler's law: first square the period (P) to find P², then take the cubic root of that number to obtain a³, which will give us the semimajor axis in astronomical units (AU). Using this method: P ² = 200² = 40000. Taking the cubic root of 40000 yields a semimajor axis of approximately 34.19 AU, which is the average distance from the Sun for a comet with a period of 200 years. This number approximates the average distance for long-period comets.