For two identical satellites in circular motion around the Earth, which statement is true?
a. The one in the higher orbit has more kinetic energy
b. The one in the lower orbit has more total energy
c. The one in the lower orbit has less total energy
d. Both have the same total energy
d. Both have the same total energy, although I must say, those satellites must have one serious case of FOMO (Fear of Missing Out). They keep orbiting Earth, trying to impress each other with their energy levels. But in reality, they're both just in a stable orbit, minding their own satellite business. So, no need to worry about who has more or less total energy because they're both equally energetic little space travelers.
The correct answer is c. The one in the lower orbit has less total energy.
Explanation:
The total energy of a satellite in circular orbit is the sum of its kinetic energy and potential energy.
The kinetic energy of an object is given by the formula: KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
In the case of two identical satellites, the mass is the same. However, the velocity of the satellite in the higher orbit is greater than the velocity of the satellite in the lower orbit. This means that the kinetic energy of the satellite in the higher orbit is greater than the kinetic energy of the satellite in the lower orbit.
The potential energy of an object is given by the formula: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference level.
Again, in the case of two identical satellites, the mass is the same. However, the height of the satellite in the higher orbit is greater than the height of the satellite in the lower orbit. This means that the potential energy of the satellite in the higher orbit is greater than the potential energy of the satellite in the lower orbit.
Since the total energy is the sum of the kinetic energy and potential energy, and both the kinetic energy and potential energy of the satellite in the higher orbit are greater than the kinetic energy and potential energy of the satellite in the lower orbit, it can be concluded that the satellite in the lower orbit has less total energy.
In order to determine which statement is true, we need to understand the concepts of kinetic energy and total energy in the context of satellites in circular motion around the Earth.
First, let's consider the concept of kinetic energy. Kinetic energy is the energy possessed by an object due to its motion. For a satellite in circular motion, the kinetic energy comes from its orbital speed.
Now, let's analyze the options:
a. The one in the higher orbit has more kinetic energy: This statement is correct. According to the formula for kinetic energy, the energy of an object in motion is directly proportional to its mass and the square of its velocity. In the case of two identical satellites, the one in the higher orbit has a greater velocity. Since the mass is the same for both satellites, the one in the higher orbit will have more kinetic energy.
b. The one in the lower orbit has more total energy: This statement is not true. Total energy includes both kinetic energy and potential energy. In the case of satellites in circular motion, the potential energy does not change as long as the radius of the orbit remains constant. So, the total energy will be the same for both satellites.
c. The one in the lower orbit has less total energy: This statement is not true, as explained above. The total energy will be the same for both satellites.
d. Both have the same total energy: This statement is the correct answer. As mentioned earlier, the total energy, which includes both kinetic energy and potential energy, will be the same for both satellites since the potential energy remains constant as long as the orbit radius remains constant.
Therefore, the correct answer is d. Both satellites have the same total energy.