Question

Earth orbits the sun in an elliptical pattern. The equation of Earth's path is.... where the measurements represent millions of kilometers. The sun is located at the focus whose coordinate is (0,0). In January, Earth is located at one of the vertices, which is 147 million kilometers from the sun. Determine Earth's distance from the sun in July.

Answer 1

General equation of Ellipse centered at (h,k) is given as

$\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1$

where a is the radius along x-axis

and b is radius along y-axis.

Given : The equation of elliptical path of Earth as

$\frac{(x+2.5)^{2}}{22350.25} + \frac{y^{2}}{22344} = 1$

Comparing the equation with the general equation, we get

(h,k) as (-2.5,0)

a = $\sqrt{22350.25} = 149.5$

b = $\sqrt{22344} = 149.48$

We have the Sun located at the coordinate (0,0).

Hence, the distance between Sun and Earth in July = 149.5 + 2.5 =152

∴ Earth's distance from the Sun in July is 152 million kilometers.