Answer
$\frac{(x+150)^2}{18062500}+\frac{y^2}{18040000}=1$
Work Step by Step
Step 1. Use the figure given in the Exercise, with the origin at the Earth's center, we can find the two vertices as $(3960+140, 0)$ or $(4100, 0)$ and $(-3960-440, 0)$ or $(-4400, 0)$
Step 2. The center of the ellipse is the midpoint between the vertices $(\frac{4100-4400}{2},0)$, thus we have the ellipse center as $C(-150,0)$
Step 3. The distance between the vertices $2a=4400+4100$ so we have $a=4250$ and $a^2=18062500$
Step 4. As the origin is a focus, we have $c=150$ (distance between origin and the ellipse center)
Step 5. Use the relationship $a^2=b^2+c^2$, we have $b^2=4250^2-150^2=18040000$
Step 6. We can write the equation of the ellipse as $\frac{(x+150)^2}{18062500}+\frac{y^2}{18040000}=1$
