Question

In 1996, astronomers discovered an icy object beyond Pluto with a semimajor axis of 84 AU. According to Kepler's third law, what is its orbital period in years?

a) 233 years

b) 265 years

c) 298 years

d) 324 years

Answer 1

The orbital period of the icy object 1996 TL 66 with a semimajor axis of 84 AU can be calculated using Kepler's third law, resulting in an approximate period of 350 years.

Step-by-step explanation:

The question focuses on calculating the orbital period of an object (1996 TL 66) discovered in 1996, which has a semimajor axis of 84 AU, using Kepler's third law. This law states that the square of the orbital period (P) is proportional to the cube of the semimajor axis (a) of its orbit. In mathematical terms, this is expressed as P2 ≈ a3. To find the orbital period, we must take the cube root of the semimajor axis cubed and then square root that number to get the orbital period in Earth years (Keplerian period). In this example, the calculation is √(843), which does not equal to any of the answer choices given in the list (233, 265, 298, 324), but rather, the correct calculation leads to approximately 353.6 years, which is roughly 350 years.