Answer
$\frac{x^2}{2.2500\times10^{16}} +\frac{y^2}{2.2491\times10^{16}}=1$
Work Step by Step
Step 1. Assume the earth orbit has a standard ellipse equation $\frac{x^2}{a^2} +\frac{y^2}{b^2}=1 $ with a center at the middle point between the perihelion and the aphelion.
Step 2. Use the figure given in the Exercise, we have $2a=147mil+153mil=300mil$ thus $a=150mil$ km (mil for million)
Step 3. As the Sun is at one focus, we have $c=a-147mil=3mil$ km, thus $b^2=a^2-c^2=(1.5\times10^8)^2-(3\times10^6)^2=2.2491\times10^{16}$
Step 4. Conclusion: the equation of the Earth can be written as $\frac{x^2}{2.2500\times10^{16}} +\frac{y^2}{2.2491\times10^{16}}=1$
