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amm1812
3 years ago
6

Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.Th

e moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km
Mathematics
1 answer:
Darina [25.2K]3 years ago
4 0
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
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I'll do part (a) to get you started.

The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.

We also see that b = 123 as well since a = b (they are vertical angles).

Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.

c+123 = 180

c = 180-123

c = 57

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To summarize, we have these three angles

a = 123

b = 123

c = 57

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