Question

directions: carefully read the text and study the diagram below. then use the information to answer question 11.
there are at least 79 moons that orbit jupiter. jupiters regular satellites move in a disc around the planet and are the largest and closest moons. the second layer is composed of irregular satellites. they are smaller than the regular satellites, have a longer orbital period, and are much farther away.

1. using what you know about the relationship between gravity, distance, and mass, explain the cause of the orbits of the satellites around jupiter and why the second layer of satellites have a longer orbital period. (3 points)

Explanation:

• Gravity - Mass Relationship: Jupiter's large mass generates a strong gravitational pull. According to Newton's law of universal gravitation \(F = G\frac{Mm}{r^{2}}\) (where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(M\) is Jupiter's mass, \(m\) is the satellite's mass, and \(r\) is the distance between their centers), this force acts as the centripetal force that keeps the satellites in orbit.
• Orbital Period - Distance Relationship: The orbital period \(T\) of a satellite is related to its orbital radius \(r\) by Kepler's third law \(T^{2}=\frac{4\pi^{2}}{GM}r^{3}\) (for a satellite orbiting a mass \(M\)). As the second - layer satellites are farther away (\(r\) is larger), substituting into the formula shows that \(T\) (orbital period) increases.

Answer:

Jupiter's large mass creates a gravitational force that acts as the centripetal force for its satellites' orbits. Using Kepler's third law \(T^{2}=\frac{4\pi^{2}}{GM}r^{3}\), since the second - layer satellites are at a greater distance (\(r\)) from Jupiter, their orbital period \(T\) is longer.