A space station orbits Earth at a height of 250 kilometers. Earth's radius is 6,371 kilometers. If the center of Earth is considered the origin, what equation represents the station's orbit in a 2D plane?(1 point)

Question

Responses

x2+y2=40,652,141
x squared plus y squared is equal to 40 comma 652 comma 141

x2+y2=37,466,641
x squared plus y squared is equal to 37 comma 466 comma 641

x2+y2=43,837,641
x squared plus y squared is equal to 43 comma 837 comma 641

x2+y2=40,589,641

Answer 1

To find the equation representing the space station's orbit in a 2D plane, we first need to determine the distance from the center of the Earth to the space station.

1. The radius of Earth is given as \(6,371\) kilometers.
2. The height of the space station above the surface of the Earth is \(250\) kilometers.
3. Therefore, the distance from the center of the Earth to the space station is:

\[ \text{Distance} = \text{radius of Earth} + \text{height of space station} = 6,371 , \text{km} + 250 , \text{km} = 6,621 , \text{km} \]

4. In a 2D Cartesian coordinate system where the center of the Earth is at the origin, the equation of a circle representing the orbit of the space station is given by:

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

where \(r\) is the distance from the center to the orbit.

5. We need to square the distance we calculated:

\[ r^2 = (6,621 , \text{km})^2 = 43,836,741 , \text{km}^2 \]

Now, we can find that the appropriate response based on the calculation is:

\[ x^2 + y^2 = 43,837,641 \]

Thus, the answer is:

x² + y² = 43,837,641