In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler's third law?

772.65 years.

Explanation:

Semi major axis = R = 84 AU = 1.257 * 10¹³ m

According to the 3rd law of Kepler, T² = 4 π² R³ / GM

Here R is the semi major axis. G = 6.67 * 10⁻¹¹ SI units.

M is the mass of the Sun = 1.98 x 10³⁰ kg

T² = 4 (3.14) ³ (1.257 * 10¹³) ³: (6.67 * 10⁻¹¹) (1.98 x 10³⁰)

⇒ Time period = T = 2.44 x 10¹⁰ seconds

1 s = 3.17 * 10⁻⁸ years

Converting the seconds to years, T = 772.65 years.