Answer:
The average distance of the new asteroid from the Sun = (2.02 × 10⁶) km
Explanation:
The speed with which planets orbit the sun vary according to their distances from the sun or how long it takes them to orbit the sun.
The new asteroid's 557 months/46.4 years taken to orbit the sun places it in between Saturn and Uranus' speed of orbit round the sun.
Uranus takes 84 years to orbit the sun at a speed of 24.61 km/hour
Saturn takes 29.4 years to orbit the sun at a speed of 34.82 km/hour.
Doing a bit of interpolation for our new asteroid at 46.4 years,
Let the speed of the asteroid be x
84 years ----> 24.61 km/h
46.4 years ----> x km/h
29.4 years -----> 34.82 km/h
(84 - 46.4)/(46.4 - 29.4) = (24.61 - x)/(x - 34.82)
we obtain that the asteroid's speed is 31.64 km/hr
So, average speed = (total distance covered)/(time taken)
Total distance covered = circumference travelled round the sun = 2πR
where R = distance from the asteroid to the sun.
Time taken = 16700 days = 16700 × 24 hours = 400800 hours
31.64 = (2πR)/400800
2πR = 31.64 × 400800 = 12681312 km
R = 12681312/(2π) = 2018293.5 km = (2.02 × 10⁶) km
