Question

What is meant by apogee, perigee and eccentricity? How do we calculate them?

Answer 1

Hint: Perigee and apogee are the farthest and the nearest point in the elliptical path respectively and eccentricity is the measure of how much a parabola or an ellipse varies from being circular. In this case we are talking about planets revolving in an elliptical path and we need to calculate the above quantities for the elliptical path of the planets.

Complete step by step answer:
We will be calculating and defining the apogee, perigee and eccentricity for a moon’s orbit which is an elliptical path. The moon’s orbit is an elliptical path and the farthest point from the earth on the orbit is called Apogee. And the nearest point on the orbit to the earth is called Perigee.

The farthest distance between the moon and the earth is called apoapsis and the shortest distance between the moon and the earth is called periapsis. Eccentricity is the measure of deviation of a shape like ellipse or parabola or a hyperbola from being circular. Eccentricity is zero for a circle and it keeps on increasing from lesser curves. That means the bigger the eccentricity, the less curvier the shape.

Now we will calculate the above quantities so for a elliptical path, let the eccentricity be denoted by \[e\], the semi-major axis be $a$ which is the half of the greatest width of the ellipse, the apogee be $A$ and the perigee be $P$. Now the eccentricity for an ellipse is $0 \leqslant e < 1$ .
The apogee for an elliptical path is $A = a(e + 1)$.
The perigee for an elliptical path is $P = a(1 - e)$.

Note: We can calculate the eccentricity or the apogee or the perigee for any elliptical path of any planet or celestial body moving in a orbit, we considered moon for more clearance of the concepts and since moon is one of the most heavenly bodies that we can see earth’s surface. And also the eccentricity greater than one is for hyperbolic and parabolic curves.