Elliptical Orbit of a Satellite

The eccentricity of an elliptical orbit can be determined using the aphelion and perihelion distances. In this case, we have a satellite in an elliptical orbit around the Earth with an aphelion of 6Re (radius of Earth) and a perihelion of 2Re. Let's calculate the eccentricity of this orbit step by step.

Step 1: Define the terms
- Aphelion: The point in the satellite's orbit that is farthest from the Earth.
- Perihelion: The point in the satellite's orbit that is closest to the Earth.
- Eccentricity: A measure of how elongated an ellipse is. It is defined as the ratio of the distance between the foci of the ellipse to its major axis length.

Step 2: Calculate the major axis length (2a)
The major axis is the longest diameter of the ellipse. In this case, the aphelion is 6Re and the perihelion is 2Re. The major axis length can be calculated as:

2a = aphelion + perihelion
= 6Re + 2Re
= 8Re

Step 3: Calculate the distance between the foci (2c)
The distance between the foci of the ellipse can be calculated using the formula:

2c = 2a * eccentricity

Since the distance between the foci is not given, let's assume it to be 'd'.

2c = d

Step 4: Calculate eccentricity (e)
The eccentricity can be calculated by dividing the distance between the foci (2c) by the major axis length (2a).

e = 2c / 2a
= d / 8Re

Step 5: Final Calculation
To determine the eccentricity, we need the value of 'd'. However, without this information, we cannot calculate the exact eccentricity.

Therefore, it is not possible to determine the eccentricity of the satellite's orbit without knowing the distance between the foci.

Conclusion:
To calculate the eccentricity of an elliptical orbit, we need to know the distance between the foci of the ellipse. Without this information, it is not possible to determine the exact eccentricity.

E =1/2