Final answer:
To estimate the length of Neptune's orbit, we can use the formula for circumference and the average distance of Neptune from the sun. Through calculations, the estimated length of Neptune's orbit is approximately 2.83 × 10^13 km.
Step-by-step explanation:
To estimate the length of Neptune's orbit, we need to calculate the circumference of its orbit. The formula for circumference is C = 2πr, where r is the radius of the orbit. In this case, the average distance of Neptune from the sun is given as 4.5 × 10^9 km. To convert this to meters, we multiply by 1000 to get 4.5 × 10^12 m.
Now, we can calculate the circumference using C = 2πr. Plugging in the value of r, we get C = 2π(4.5 × 10^12) = 2π × 4.5 × 10^12 = 2 × 3.1416 × 4.5 × 10^12 = 28.274 × 10^12 ≈ 2.83 × 10^13 meters.
Therefore, the estimated length of Neptune's orbit is approximately 2.83 × 10^13 km.