Question

objects orbiting around the center of the milky way obey keplers 3rd law. this means that:
please select the best choice from the available options.
larger clusters of stars will orbit the center more quickly than smaller ones
the orbits of all objects around the galaxy are in the shape of a perfect circle
the pull of gravity gets stronger and stronger as you get further away from the center
the closer a star is to the center, the longer it will take to go around
a cloud of gas or star that is further from the center will generally take more time to orbit

Explanation:

Kepler's 3rd Law states that \(T^{2}\propto r^{3}\), where \(T\) is the orbital period and \(r\) is the orbital radius. This means that objects further from the center (larger \(r\)) have longer orbital periods (\(T\)).

• For the first option: Larger clusters (assuming this refers to distance, not mass in a wrong - way interpretation) would have longer periods, not quicker orbits.
• The second option: Kepler's first law states that orbits are ellipses, not perfect circles.
• The third option: Gravity \(F = \frac{GMm}{r^{2}}\) (from Newton's law of gravitation, which is consistent with Kepler's laws in the context of orbital motion), so gravity gets weaker as \(r\) increases.
• The fourth option: Closer stars (smaller \(r\)) have shorter orbital periods (\(T\)) according to \(T^{2}\propto r^{3}\).
• The fifth option: Since \(T^{2}\propto r^{3}\), a cloud of gas or star further from the center (\(r\) is larger) will have a larger \(T\) (longer orbital period).

Answer:

a cloud of gas or star that is further from the center will generally take more time to orbit