We have
SinC/ c = Sin A / a
Sin 71/ 26 = Sin A / 27
Sin A = 27 Sin 71 / 26 = about .982
So°
Sin-1(.982) = A = 79. 08°
Then angle B = 180 - 71 - 79.08 = 29.92°
And b is given by
b/sin29.92 = 26/sin 71
b = 26sin29.92/sin71 = about 13.72
But A could also be an obtuse angle = 180 - 79.08 = 100.92°
So we have
B = 180 - 71 - 100.92 = 8.08°
And we have
b / sin 8.08 = 26/sin71
b = 26sin8.08/sin 71 = 3.865
I believe the phi ratio^2 = 1 + phi ratio
phi ratio = 1.6180339
phi ratio^2 = 2.6180339
An equation for the ellipse ( standard form ):
x²/a² + y²/b² = 1
Here is: a - semi-major axis and b - semi-minor axis.
Radius of the moon is 1,000 km and the distance from the surface of the moon to the satellite varies from 953 km to 466 km.
a = 1,000 + 953 = 1,953 km
b = 1,000 + 466 = 1,466 km
Answer:
The equation is x² / 1,953² + y² / 1,466² = 1
or: x²/3,814,209 + y²/2,149,156 = 1
