Problem 83. The central attractive force F on an earth satellite can have no moment about the center O of the earth. For the particular elliptical orbit with major and minor axes as shown, a satellite will have a velocity of 33 880 km/h at the perigee altitude of 390 km. Determine the velocity of the satellite at point B and at apogee A. The radius of the earth is 6371 km. 11 720 km -13 520 km 33 880 km/h. P 390 km

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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**Problem 83.** The central attractive force \( F \) on an earth satellite can have no moment about the center \( O \) of the earth. For the particular elliptical orbit with major and minor axes as shown, a satellite will have a velocity of \( 33{,}880 \text{ km/h} \) at the perigee altitude of \( 390 \text{ km} \). Determine the velocity of the satellite at point \( B \) and at apogee \( A \). The radius of the earth is \( 6371 \text{ km} \).

**Diagram Explanation:**

The diagram illustrates an elliptical orbit around the Earth. The Earth is shown as a circle at the center labeled \( O \). The elliptical orbit is represented as an elongated dashed circle surrounding the Earth. Key points labeled on the elliptical orbit include:

- **Perigee \( P \)**: The point where the satellite is closest to the Earth. The velocity at this point is given as \( 33{,}880 \text{ km/h} \) and the altitude above Earth at this point is \( 390 \text{ km} \).

- **Apogee \( A \)**: The point where the satellite is farthest from the Earth. The distance from Earth's center to this point is shown as \( 13{,}520 \text{ km} \).

- **Point \( B \)**: Positioned at a different location on the elliptical path with a vertical distance of \( 11{,}720 \text{ km} \) from the center.

The overall geometry demonstrates the varying distance of the satellite from Earth at different orbital positions, which affects its velocity due to gravitational attraction.
Transcribed Image Text:**Problem 83.** The central attractive force \( F \) on an earth satellite can have no moment about the center \( O \) of the earth. For the particular elliptical orbit with major and minor axes as shown, a satellite will have a velocity of \( 33{,}880 \text{ km/h} \) at the perigee altitude of \( 390 \text{ km} \). Determine the velocity of the satellite at point \( B \) and at apogee \( A \). The radius of the earth is \( 6371 \text{ km} \). **Diagram Explanation:** The diagram illustrates an elliptical orbit around the Earth. The Earth is shown as a circle at the center labeled \( O \). The elliptical orbit is represented as an elongated dashed circle surrounding the Earth. Key points labeled on the elliptical orbit include: - **Perigee \( P \)**: The point where the satellite is closest to the Earth. The velocity at this point is given as \( 33{,}880 \text{ km/h} \) and the altitude above Earth at this point is \( 390 \text{ km} \). - **Apogee \( A \)**: The point where the satellite is farthest from the Earth. The distance from Earth's center to this point is shown as \( 13{,}520 \text{ km} \). - **Point \( B \)**: Positioned at a different location on the elliptical path with a vertical distance of \( 11{,}720 \text{ km} \) from the center. The overall geometry demonstrates the varying distance of the satellite from Earth at different orbital positions, which affects its velocity due to gravitational attraction.
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