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
To determine which statement is true, we need to understand the relationship between kinetic energy, potential energy, and total energy of an object in circular motion.
The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
The potential energy of an object in circular motion is given by the formula PE = -G * (m * M) / r, where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the object and the center of the Earth.
In the case of two identical satellites in circular motion around the Earth, their masses are the same, and their velocities are also the same because the circular orbits have the same circumference. However, their distances from the Earth's center are different, as one is in a higher orbit and the other is in a lower orbit.
Now let's analyze each statement:
a. The one in the higher orbit has more kinetic energy:
Since the velocity of the satellites is the same, and kinetic energy depends on the square of the velocity, the statement is incorrect. Both satellites have the same kinetic energy.
b. The one in the lower orbit has more total energy:
Total energy is the sum of kinetic energy and potential energy. If the lower orbit satellite has more potential energy due to its shorter distance from the Earth's center, then the statement is correct. The potential energy contributes to the total energy.
c. The one in the lower orbit has less total energy:
As explained above, the lower orbit satellite has more potential energy, and since the total energy includes both kinetic and potential energy, this statement is incorrect.
d. Both have the same total energy:
This statement is incorrect because the potential energy differs based on the distance from the Earth's center. Therefore, the total energy will also differ between the satellites.
Based on the analysis, the correct statement is b. The one in the lower orbit has more total energy.