For an elliptic Earth orbit find the ratio of the time required to travel from a point on the lower latus parameter (ν = −π/3) to the opposite point on the upper latus parameter (ν = π/2) compared to the orbit period. Express the result as a function of the orbit eccentricity e as the only variable. Check the result as e → 0 and verify that the vanishing of the eccentricity produces the expected result

For an elliptic Earth orbit find the ratio of the time required to travel from a point on the lower latus parameter (ν = −π/3) to the opposite point on the upper latus parameter (ν = π/2) compared to the orbit period. Express the result as a function of the orbit eccentricity e as the only variable. Check the result as e → 0 and verify that the vanishing of the eccentricity produces the expected result