when is the Kinetic energy of the satellite the greatest and the least?
Potential energy the greatest? The least?
The kinetic energy of a satellite is the greatest when it is closest to the body it is orbiting, and the least when it is farthest from the body.
On the other hand, the potential energy of a satellite is the greatest when it is farthest from the body it is orbiting, and the least when it is closest to the body.
In order to determine when the kinetic energy and potential energy of a satellite are greatest and least, we need to understand how these energy values change with respect to the satellite's position and velocity.
Let's break it down:
1. Kinetic energy of a satellite:
The kinetic energy of a satellite is directly related to its velocity. The formula for kinetic energy is KE = (1/2) * m * v^2, where m represents the mass of the satellite and v represents its velocity.
- Greatest kinetic energy: The kinetic energy of a satellite is greatest when its velocity is at its maximum. This typically occurs when the satellite is closest to its largest gravitational source, such as planet Earth, and is at a point in its orbit where it is moving at its highest speed. At this point, the satellite has the most kinetic energy.
- Least kinetic energy: The kinetic energy of a satellite is least when its velocity is at its minimum. This usually occurs when the satellite is at its farthest point from the gravitational source, such as the apogee (the farthest point in its elliptical orbit). At this position, the satellite has the least kinetic energy.
2. Potential energy of a satellite:
The potential energy of a satellite is related to its distance from the gravitational source and can be calculated using the formula PE = -G * (M * m) / r, where G is the gravitational constant, M is the mass of the gravitational source, m is the mass of the satellite, and r is the distance between the satellite and the gravitational source.
- Greatest potential energy: The potential energy of a satellite is greatest when it is at its highest point in the orbit, such as the apogee. At this position, the satellite is farthest from the gravitational source and has the greatest potential energy.
- Least potential energy: The potential energy of a satellite is least when it is at its lowest point in the orbit, such as the perigee (the closest point in its elliptical orbit). At this position, the satellite is closest to the gravitational source and has the least potential energy.
To summarize:
- The kinetic energy of a satellite is greatest when it is closest to the largest gravitational source, and least when it is farthest away.
- The potential energy of a satellite is greatest when it is at its highest point in the orbit, and least when it is at its lowest point.