Sid created a chart to summarize characteristics of satellite motion.
\begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{Characteristic} & \multicolumn{1}{c|}{Description} \\ \hline tangential speed & \begin{tabular}{l} remains constant throughout orbit; \\ decreases with satellite's increasing \\ distance from Earth \end{tabular} \\ \hline centripetal force & \begin{tabular}{l} parallel to the velocity of satellite; does \\ not speed up or slow down satellite \end{tabular} \\ \hline centripetal acceleration & \begin{tabular}{l} always points toward Earth; exists \\ because satellite is always changing \\ direction \end{tabular} \\ \hline \end{tabular}
Which best describes Sid's error?
A. Tangential speed changes throughout a satellite's orbit. B. Centripetal force is perpendicular to the velocity of the satellite. C. Tangential speed increases with a satellite's increasing distance from Earth. D. Centripetal force can sometimes slow down a satellite in orbit.
Let's analyze the statements provided by Sid in the chart against the correct principles of satellite motion.
1. Tangential speed: - Sid states that the tangential speed "remains constant throughout orbit" and "decreases with satellite's increasing distance from Earth." - This is generally true for a circular orbit where the tangential speed remains constant. For elliptical orbits, the speed varies but is overall greater when the satellite is closer to Earth. Hence, the statement about varying speed with distance could be considered in the context of elliptical orbits but typically in the context provided, the focus on constancy is valid.
2. Centripetal force: - Sid states that centripetal force is "parallel to the velocity of satellite" and "does not speed up or slow down the satellite." - This is incorrect. The centripetal force is always directed towards the center of the circular path, which is towards the Earth for satellite motion. This means that the centripetal force acts perpendicular to the tangential velocity of the satellite.
3. Centripetal acceleration: - Sid states that centripetal acceleration "always points toward Earth" and "exists because the satellite is always changing direction." - This is a correct statement. The centripetal acceleration is directed towards the center of the Earth's mass and is responsible for changing the direction of the satellite's velocity to keep it in orbit.
Given the descriptions of potential errors:
1. Tangential speed changes throughout a satellite’s orbit. 2. Centripetal force is perpendicular to the velocity of the satellite. 3. Tangential speed increases with a satellite’s increasing distance from Earth. 4. Centripetal force can sometimes slow down a satellite in orbit.
The best description of Sid's error is:
Centripetal force is perpendicular to the velocity of the satellite.
The correct interpretation of centripetal force is that it is always perpendicular to the velocity, providing the necessary centripetal acceleration to change the direction of the velocity vector, thereby keeping the satellite in its curved path.
