The asteroid revolves around the Sun with a period of 410 days. Determine the distance from the asteroid to the Sun.

Let’s use Kepler’s law:
(T1) ^ 2 / (T2) ^ 2 = (a1) ^ 3 / (a2) ^ 3, T1 is the Earth’s orbital period, T1 = 365 days, T2 = 410 days is the asteroid’s orbital period, a1 is the distance from the Earth to the Sun , a2 – from the asteroid to the Sun.
Then we find:
(a2) ^ 3 = ((a1) ^ 3) × ((T2) ^ 2) / ((T1) ^ 2) ~ ((a1) ^ 3) × 1.26 ~ 1.26 a.u.
Answer: 1.26 au