Satellite Motion Characteristics in Circular Orbit

Let's analyze the motion of a satellite in a circular orbit around the Earth.

Understanding Circular Orbits

A circular orbit means the satellite travels in a perfect circle around the Earth at a constant altitude. This implies the distance from the center of the Earth remains constant.

Analyzing Velocity and Speed

In physics, velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Speed is just the magnitude of the velocity.

• In a circular orbit, the satellite's distance from the Earth is constant, and assuming no external forces slow it down (like atmospheric drag), its speed remains constant.
• However, because the satellite is moving in a circle, its direction of motion is constantly changing. The velocity vector is always tangent to the circular path. As the direction changes, the velocity vector itself changes, even if its magnitude (speed) does not.

Therefore, a satellite in a circular orbit has a constant speed but a changing velocity.

Evaluating the Options

Option 1: Zero acceleration

Acceleration is defined as the rate of change of velocity. Since the satellite's velocity is changing (due to its changing direction), it must be experiencing acceleration. This acceleration is directed towards the center of the Earth and is called centripetal acceleration. It's responsible for keeping the satellite in its circular path.

The formula for centripetal acceleration is given by: $a = \frac{v^2}{r}$ where $v$ is the constant speed and $r$ is the radius of the orbit. Since $v$ and $r$ are constant, the magnitude of the acceleration is constant, but its direction continuously changes, pointing towards the center of the Earth. Thus, the acceleration is not zero.

Option 2: Constant speed but changing velocity

As explained above, this accurately describes the motion in a uniform circular orbit. The magnitude of the velocity (speed) is constant, but the direction changes continuously, making the velocity vector change.

Option 3: Constant velocity

This is incorrect because, as detailed earlier, the direction of the velocity vector changes continuously in a circular orbit.

Option 4: Decreasing energy

For a satellite in an ideal orbit (neglecting external factors like drag or gravitational influence from other bodies), its total mechanical energy (sum of kinetic and potential energy) is conserved, meaning it remains constant. The kinetic energy ($KE = \frac{1}{2}mv^2$) is constant because the speed ($v$) is constant. The potential energy ($PE = -\frac{GMm}{r}$) is also constant because the orbital radius ($r$) is constant. Therefore, the total energy does not decrease.

Conclusion

Based on the analysis, the defining characteristic of a satellite moving in a circular orbit is that its speed is constant, but its velocity is continuously changing due to the alteration in direction.