Question

To transfer a satellite from an elliptical orbit into a circular orbit having a radius equal to the apogee distance of the elliptical orbit, then the speed of the satellite should be

• A. increased at the apogee
• B. decreased at the apogee
• C. increased at the perigee
• D. decreased at the perigee

Hint:

Hohmann transfer orbits involve burns at perigee and apogee to adjust orbit shapes.

Answer 1

The Correct Option is A

To transfer a satellite from an elliptical orbit into a circular orbit at the apogee, we need to understand the concept of orbital mechanics. An elliptical orbit has two key points: the perigee, the closest point to the planet, and the apogee, the farthest point.

Step 1: Identify the current speed of the satellite at the apogee of the elliptical orbit. The velocity \( V_{\text{elliptical}}\) at apogee can be determined using the vis-viva equation:

\[ V_{\text{elliptical}} = \sqrt{\mu \left(\frac{2}{r_{a}} - \frac{1}{a}\right)} \]

where \( \mu \) is the gravitational parameter of the planet, \( r_{a} \) is the apogee distance, and \( a \) is the semi-major axis of the elliptical orbit.

Step 2: Compute the desired speed for a circular orbit at apogee. For a circular orbit, the velocity \( V_{\text{circular}} \) is given by:

\[ V_{\text{circular}} = \sqrt{\frac{\mu}{r_{a}}} \]

Step 3: To achieve a circular orbit, the speed of the satellite needs to be increased from \( V_{\text{elliptical}} \) to \( V_{\text{circular}} \) precisely at the apogee.

Conclusion: Thus, to transition from an elliptical to a circular orbit at the apogee distance, the speed of the satellite should be increased at the apogee.