Answer:
The average distance of the new asteroid from the Sun is estimated to be (2.02 × 10⁶) km.
Explanation:
The orbital speed of planets varies based on their distance from the Sun, which also affects their orbital period.
With its 557 months, equivalent to 46.4 years for an orbit around the Sun, the new asteroid's speed is situated between the orbital speeds of Saturn and Uranus.
Uranus orbits the Sun in 84 years at 24.61 km/hour,
while Saturn completes its orbit in 29.4 years at 34.82 km/hour.
To interpolate the speed for our asteroid at 46.4 years,
we denote its speed as x.
84 years ----> 24.61 km/h
46.4 years ----> x km/h
29.4 years -----> 34.82 km/h
Setting up the proportion:
(84 - 46.4)/(46.4 - 29.4) = (24.61 - x)/(x - 34.82)
Solving for x gives the asteroid's speed as 31.64 km/hr.
To find the average speed, use the formula:
Average speed = (total distance)/(time taken).
The total distance covered equals the circumference of the orbit around the Sun = 2πR,
where R = distance from the asteroid to the Sun.
Time taken = 16700 days = 16700 × 24 hours = 400800 hours.
Thus, we find that 31.64 = (2πR)/400800.
From this, we get 2πR = 31.64 × 400800 = 12681312 km.
And, R = 12681312/(2π) = 2018293.5 km = (2.02 × 10⁶) km.
