A body describing an ellipse of eccentricity e = 0.4 under the action of a force tending toward a focus, and when it is at the near apsis the center of force is transferred to the other focus. The eccentricity of the new orbit will be
a) 0.52
b) 0.78

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

Learn how to calculate the new eccentricity of an elliptical orbit when the center of force is transferred between foci. This problem involves orbital mechanics and ellipse properties, with a detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation