Question

The moon's orbit around the Earth is elliptical with the Earth at one focus and with eccentricity 0.0059. If the distance between the moon and Earth at the closest point is 363 300 km, determine the distance at the farthest point. Round to the nearest 100 km.

Answer 1

Answer:

367600km

Step-By-Step Explanation

Planets, moon and satellites follow elliptic orbits..

• The eccentricity 0≤e<1 describes the shape of the ellipse where an eccentricity of zero is a perfect circle.

• The furthest distance of the Moon from the Earth in its orbit is called the Apogee.

• The closest distance of the Moon from the Earth in its orbit is called the Perigee.  

The Apogee (A), and Perigee(P) is related to the semi-major axis(a) of the ellipse and its eccentricity by the equations:

A=a(1+e)  ……(1)

P=a(1−e)   ……(2)

The closest distance Perigee, P=363 300 km

Eccentricity, e = 0.0059.

From Equation 2, $a=\frac{P}{1-e}$

$a=\frac{363300}{1-0.0059}=\frac{363300}{0.9941}=365456.19[/$

Using a=365456.19km in Equation (1)

The furthest distance, $A=365456.19 (1+0.0059) \\=365456.19 (1.0059) \\=367612.38 \approx 367600 km (\text{to the nearest 100km}$