Problem 2 The following figure shows two satellites in Earth orbits: Satellite A is in a circular orbit with an altitude of 9,622 km , while Satellite B is in an elliptical orbit with an apogee altitude of 9,622 km . At the instant shown in Figure P2, Satellite B is passing through the apogee while Satellite A is ahead of Satellite B with an angular separation of 120deg

Applications and Investigations in Earth Science (9th Edition)
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Chapter1: The Study Of Minerals
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**Problem 2**

The following figure illustrates two satellites in Earth orbits:

- **Satellite A** is in a circular orbit with an altitude of **9,622 km**.
- **Satellite B** is in an elliptical orbit with an apogee altitude of **9,622 km**.

In the scenario depicted, **Satellite B** is passing through the apogee while **Satellite A** is ahead of **Satellite B** with an angular separation of **120 degrees**.

**Task:**

Determine the perigee altitude of the elliptical orbit so that Satellites A and B occupy the same radial position when Satellite A first arrives at the apogee point. In other words, Satellites A and B perform a rendezvous maneuver at the apogee of Satellite B.

**Diagram Explanation:**

The image shows two satellite orbits around the Earth:

1. **Satellite A** is on a circular path, consistent in altitude.
2. **Satellite B’s** orbit is elliptical, with the farthest point (apogee) at the same altitude as Satellite A's orbit.
3. An angle of 120 degrees marks the distance ahead Satellite A is relative to Satellite B at the moment depicted. The Earth is centered in the diagram. 

Understanding this setup is crucial for calculating the desired perigee altitude to synchronize the satellites’ positions.
Transcribed Image Text:**Problem 2** The following figure illustrates two satellites in Earth orbits: - **Satellite A** is in a circular orbit with an altitude of **9,622 km**. - **Satellite B** is in an elliptical orbit with an apogee altitude of **9,622 km**. In the scenario depicted, **Satellite B** is passing through the apogee while **Satellite A** is ahead of **Satellite B** with an angular separation of **120 degrees**. **Task:** Determine the perigee altitude of the elliptical orbit so that Satellites A and B occupy the same radial position when Satellite A first arrives at the apogee point. In other words, Satellites A and B perform a rendezvous maneuver at the apogee of Satellite B. **Diagram Explanation:** The image shows two satellite orbits around the Earth: 1. **Satellite A** is on a circular path, consistent in altitude. 2. **Satellite B’s** orbit is elliptical, with the farthest point (apogee) at the same altitude as Satellite A's orbit. 3. An angle of 120 degrees marks the distance ahead Satellite A is relative to Satellite B at the moment depicted. The Earth is centered in the diagram. Understanding this setup is crucial for calculating the desired perigee altitude to synchronize the satellites’ positions.
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