Answer:
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.
