Question

Question

Apollo 8 orbited the moon in a circular orbit. Its average altitude was 185 km above the moon's surface. Create an equation to model the path of Apollo 8 using the center of the moon as the origin. Note that the radius of the moon is 1,737 km.
(1 point)
Responses

x squared plus y squared equals 34,225
Image with alt text: x squared plus y squared equals 34,225

x squared plus y squared equals 2,408,704
Image with alt text: x squared plus y squared equals 2,408,704

x squared plus y squared equals 3,017,169
Image with alt text: x squared plus y squared equals 3,017,169

x squared plus y squared equals 3,694,084
Image with alt text: x squared plus y squared equals 3,694,084
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Answer 1

To model the path of Apollo 8 as it orbited the moon, we need to account for both the radius of the moon and the altitude at which Apollo 8 orbited.

1. The radius of the moon is given as 1,737 km.
2. Apollo 8's average altitude was 185 km above the moon's surface.

To find the total distance from the center of the moon to Apollo 8, we add the altitude to the radius of the moon:

\[ \text{Total radius} = \text{Radius of the moon} + \text{Altitude} = 1,737 , \text{km} + 185 , \text{km} = 1,922 , \text{km} \]

The equation of a circle in the coordinate plane with center at the origin is given by:

\[ x^2 + y^2 = r^2 \]

where \( r \) is the radius of the circle. In this case, we have:

\[ r = 1,922 , \text{km} \]

Now we can calculate \( r^2 \):

\[ r^2 = (1,922)^2 = 3,694,084 \]

Thus, the equation that models the path of Apollo 8 is:

\[ x^2 + y^2 = 3,694,084 \]

So the correct response is:

x squared plus y squared equals 3,694,084.