the Rings of Neptune. Recent observations of Voyager I and II showed that Neptune’s ring system is more complex than had been believed.

Question

For one thing, it is made up of a large number of distinguishable rings rather than one continuous great ring as was previously though. The outermost ring, 1989N1R, has an inner radius of approximately 62,900 km (measured from the center of the planet) and a radial width of approximately 50 km.

A) Use these data to estimate the area of the ring using differential calculus.

Answer 1

Given inner radius R_inner and the radial width ΔR, treat the ring as a thin circular annulus and calculate its area.

Area of a circle is A = πr². Using differentials, area of the annulus is:

dA = 2πR_inner*ΔR

dA = 2π * 62,900 * 50 = 19,795,400 km² (approximately)

So, the area of the ring is approximately 19,795,400 km².

Hope this was helpful.