Question

If the distance between two foci of a moon's orbit is 6.8 and the length between the major axis is 11.9, calculate the eccentricity of the moon's orbit.

Answer 1

The eccentricity of the moon's orbit is approximately 0.44.

The eccentricity (e) of an orbit is a measure of how elliptical or circular it is. In the case of a moon's orbit, the eccentricity can be calculated using the formula
`e=√(1-b^2/a^2)`, where a is the semi-major axis (half the length of the major axis) and b is the semi-minor axis (half the length of the minor axis). In this scenario, the major axis is given as 11.9, and the distance between the two foci (2c) is given as 6.8.

The semi-major axis a is calculated as a= 1/2×(11.9), and the semi-minor axis b is calculated as
`b=1/2√(a^2-c^2)`, where c is the distance from the center to one of the foci. With these values, the eccentricity is determined using the provided formula, resulting in an eccentricity of approximately 0.44 for the moon's orbit. This value indicates a moderately elliptical orbit for the moon around its primary body.