To solve for the new eccentricity of the orbit after the center of force is transferred to the other focus, we need to use the properties of elliptical orbits.

Given Data

• Initial eccentricity $e = 0.4$

Solution

1. Initial Orbit Parameters:

   • For the initial ellipse, the distance from the center to the focus (c) is related to the semi-major axis (a) and eccentricity (e) by: $c = ae$
   • Semi-major axis remains the same during the transfer of the focus.

2. Effect of Transferring Focus:

   • When the center of force is transferred to the other focus, the body will describe a new ellipse with the same semi-major axis, but the other focus becomes the new center of attraction.
   • This implies the old apoapsis (farthest point from the initial focus) becomes the new periapsis (closest point to the new focus), and vice versa.

3. Determine the New Eccentricity:

   • The new semi-major axis (a') is the same as the original semi-major axis (a).
   • Let the new semi-major axis be $a'$ and the new eccentricity be $e'$.
   • The