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 1,737 km.
a. x^2+y^2=34,225
b. x^2+y^2=2,408,704
c. x^2+y^2=3,017,169
d. x^2+y^2=3,694,084
I am a little confused with this. Please help ;)
Correction.
I forgot altitude.
R = r + 185 = 1,737 + 185 = 1,922
x² + y² = R²
x² + y² = 1,922²
x² + y² = 3,694,084
Answer d.
Bosian is 100% correct for x² + y² = 3,694,084
Answer d.
As for rest correct answers are
1. B (x-4)^2+(y+5)^2=4
2. C (x+2)^2+(y-2)^2=13
I believe that is correct. It matches what I did on paper.
To model the path of Apollo 8 using the center of the moon as the origin, we can use the equation of a circle. The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the moon is the origin, which means (h, k) = (0, 0). The radius of the moon is 1,737 km, so we can substitute r = 1,737 into the equation:
x^2 + y^2 = (1,737)^2
Simplifying the equation further:
x^2 + y^2 = 3,017,169
Hence, the equation that models the path of Apollo 8 orbiting the moon in a circular orbit is:
c. x^2 + y^2 = 3,017,169
What is difficult here?
Equation of a circle:
x² + y² = r²
x² + y² = 1,737²
x² + y² = 3,017,169
Answer c.