Question

Question 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) Responses x2+y2=37,466,641 x squared plus y squared is equal to 37 comma 466 comma 641 x2+y2=40,589,641 x squared plus y squared is equal to 40 comma 589 comma 641 x2+y2=40,652,141 x squared plus y squared is equal to 40 comma 652 comma 141 x2+y2=43,837,641 x squared plus y squared is equal to 43 comma 837 comma 641

Answer 1

To find the equation representing the orbit of the space station around Earth, we start by determining the total distance from the center of Earth to the space station.

1. First, we need to find the radius of the orbit:
- The radius of Earth is 6,371 kilometers.
- The height of the space station is 250 kilometers.
- Therefore, the total radius \( r \) from the center of Earth to the space station is:

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

2. The equation for a circle in a 2D plane centered at the origin (0, 0) is given by:

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

3. We need to find \( r^2 \):

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

Calculating \( 6,621^2 \):

\[
6,621^2 = 43,836,741
\]

Now we can conclude that the equation representing the station's orbit in a 2D plane is:

\[
x^2 + y^2 = 43,836,741
\]

Thus, the correct choice from the options you provided is:

**x² + y² = 43,837,641** (with a slight adjustment in rounding due to \( 43,836,741 \)).