Calculate the speed (in m/s) of a satellite in an orbit, H= 3599km above the Earth's surface. Radius of the Earth, R = 6.38 x 10 ^ 6 m,Mass of the Earth, M=5.98x10 ^ 24 kg.
Calculate the speed (in m/s) of a satellite in an orbit, H= 3599km above the Earth's surface. Radius of the Earth, R = 6.38 x 10 ^ 6 m,Mass of the Earth, M=5.98x10 ^ 24 kg.
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Calculate the speed (in m/s) of a satellite in an orbit, H= 3599km above the Earth's surface. Radius of the Earth, R = 6.38 x 10 ^ 6 m,Mass of the Earth, M=5.98x10 ^ 24 kg.
![### Understanding Orbital Mechanics: Satellite Orbit Around Earth
#### Diagram Explained
The image provided is a simplified diagram illustrating a satellite in orbit around Earth. Key components of the diagram are:
1. **Earth**: Depicted as a blue sphere at the center of the diagram. Earth acts as the focal point around which satellites orbit.
2. **Satellite**: Positioned along the orbital path around Earth.
3. **Orbital Path**: Represented by a circular line around Earth, indicating the path that the satellite follows.
4. **Radius (r)**: A line extending from the center of Earth to the satellite, labeled as ‘r’. This represents the radius of the satellite’s orbit, which is the distance from the center of Earth to the satellite.
5. **Velocity (v)**: An arrow labeled 'v' pointing tangentially to the orbital path of the satellite. This indicates the direction and speed at which the satellite is moving around Earth. In orbital mechanics, velocity is usually tangent to the path of motion.
6. **Force (F)**: An arrow labeled 'F' pointing from the satellite to the center of Earth. This represents the gravitational force exerted by Earth on the satellite. It is directed toward the center of the Earth, following Newton's law of universal gravitation.
#### Key Concepts
1. **Gravitational Force (F)**:
- This is the force pulling the satellite towards Earth’s center.
- It is responsible for keeping the satellite in its orbit.
- Calculated by Newton's law of gravitation:
\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]
where \( G \) is the gravitational constant, \( m_1 \) is the mass of Earth, \( m_2 \) is the mass of the satellite, and \( r \) is the distance between the satellite and Earth's center.
2. **Orbital Velocity (v)**:
- The satellite needs to maintain a specific velocity to stay in orbit.
- Too fast, and the satellite would escape Earth's gravity. Too slow, and it would fall back to Earth.
- The balance between gravitational force and the tangential speed of the satellite results in a stable orbit.
3. **Centripetal Force**:
- The gravitational force acts as a centripetal force, constantly pulling the satellite](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81610fbc-71d4-4f51-a970-c974c7e9c894%2F5aef72a4-83e5-4e62-adbf-b4235ea196b7%2Fygmcqqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Orbital Mechanics: Satellite Orbit Around Earth
#### Diagram Explained
The image provided is a simplified diagram illustrating a satellite in orbit around Earth. Key components of the diagram are:
1. **Earth**: Depicted as a blue sphere at the center of the diagram. Earth acts as the focal point around which satellites orbit.
2. **Satellite**: Positioned along the orbital path around Earth.
3. **Orbital Path**: Represented by a circular line around Earth, indicating the path that the satellite follows.
4. **Radius (r)**: A line extending from the center of Earth to the satellite, labeled as ‘r’. This represents the radius of the satellite’s orbit, which is the distance from the center of Earth to the satellite.
5. **Velocity (v)**: An arrow labeled 'v' pointing tangentially to the orbital path of the satellite. This indicates the direction and speed at which the satellite is moving around Earth. In orbital mechanics, velocity is usually tangent to the path of motion.
6. **Force (F)**: An arrow labeled 'F' pointing from the satellite to the center of Earth. This represents the gravitational force exerted by Earth on the satellite. It is directed toward the center of the Earth, following Newton's law of universal gravitation.
#### Key Concepts
1. **Gravitational Force (F)**:
- This is the force pulling the satellite towards Earth’s center.
- It is responsible for keeping the satellite in its orbit.
- Calculated by Newton's law of gravitation:
\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]
where \( G \) is the gravitational constant, \( m_1 \) is the mass of Earth, \( m_2 \) is the mass of the satellite, and \( r \) is the distance between the satellite and Earth's center.
2. **Orbital Velocity (v)**:
- The satellite needs to maintain a specific velocity to stay in orbit.
- Too fast, and the satellite would escape Earth's gravity. Too slow, and it would fall back to Earth.
- The balance between gravitational force and the tangential speed of the satellite results in a stable orbit.
3. **Centripetal Force**:
- The gravitational force acts as a centripetal force, constantly pulling the satellite
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