Question

The planet Neptune is the farthest planet from the Sun. A satellite is orbiting around Neptune at a distance of 180 km. As the satellite orbits, only a portion of the planet may be seen at one time. This is referred to as the horizon circle and denoted by the variable 2004-05-03-06-00_files/i0260001.jpg. The distance between the satellite and the horizon circle 2004-05-03-06-00_files/i0260002.jpg is 2,992 km. Find the approximate diameter of the planet Neptune. Round your final answer to the nearest kilometer.

Answer 1

2,992² + r² = ( r + 180 )²
8,952,064 + r² = r² + 360 r + 32,400
360 r = 8,952,064 - 32,400
360 r = 8,919,664
r = 8,919,664 : 360
r = 24,776.844 km
d = 24,776.844  ·  2 = 49,553688 ≈ 49,554 km
Answer:
The approximate diameter of the planet Neptune is 49,554 km.