Explanation:

When a satellite orbits as close to the Earth's surface as possible, several factors come into play that affect its speed, time period of rotation, and the total energy of the Earth plus satellite system.

a) Speed is maximum:

When a satellite orbits closer to the Earth's surface, the gravitational force acting on it is stronger. According to Newton's law of universal gravitation, the force of gravity is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them. As the distance between the satellite and the Earth's surface decreases, the gravitational force increases.

To maintain a stable orbit, the satellite must balance this gravitational force with its centripetal force. The centripetal force is provided by the satellite's velocity. As the gravitational force increases, the satellite must travel at a higher speed to maintain its orbit. Therefore, when a satellite orbits as close to the Earth's surface as possible, its speed is maximum.

b) Time period of rotation is minimum:

The time period of rotation of a satellite is the time it takes to complete one orbit around the Earth. It depends on the satellite's speed and the circumference of its orbit.

As mentioned earlier, when a satellite orbits closer to the Earth's surface, its speed increases. The circumference of the orbit remains the same regardless of the satellite's distance from the Earth's surface. Since the time period of rotation is determined by the ratio of the circumference to the speed, a higher speed results in a shorter time period of rotation. Therefore, when a satellite orbits as close to the Earth's surface as possible, the time period of rotation is minimum.

c) Total energy of the Earth plus satellite system is minimum:

The total energy of the Earth plus satellite system includes both the kinetic energy and the gravitational potential energy.

As the satellite orbits closer to the Earth's surface, its speed increases (as explained earlier). Kinetic energy is directly proportional to the square of the velocity. Therefore, the kinetic energy of the satellite increases.

On the other hand, the gravitational potential energy decreases as the satellite is closer to the Earth's surface due to the decrease in the distance between them. Gravitational potential energy is directly proportional to the mass, the acceleration due to gravity, and the height. As the height decreases, the gravitational potential energy decreases.

The increase in kinetic energy is greater than the decrease in gravitational potential energy, resulting in a net increase in the total energy of the system. Therefore, when a satellite orbits as close to the Earth's surface as possible, the total energy of the Earth plus satellite system is minimum.

In summary:
- When a satellite orbits as close to the Earth's surface as possible, its speed is maximum.
- The time period of rotation is minimum because of the increased speed.
- The total energy of the Earth plus satellite system is minimum due to the increase in kinetic energy and decrease in gravitational potential energy.

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