The Orbital Periods of Io,Europa,and Ganymede Are in the Ratio

question 85

Multiple Choice

The orbital periods of Io,Europa,and Ganymede are in the ratio 1:2:4.Is there any significance to this?

• A) No, this is just a random coincidence of the manner in which these satellites condensed out of the primordial nebula around Jupiter.
• B) Yes, this is the ordering predicted by Kepler's third law.
• C) Yes. Combined with the fact that these are all prograde orbits, this shows that these moons are not captured asteroids.
• D) Yes. After completion of an orbit by Ganymede, all these moons will be in a line, creating tidal stresses on Io.

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Definitions:

Utility Function

An economic model that describes how consumers rank different bundles or combinations of goods according to the level of satisfaction or utility they provide.

Equivalent Variation

A measure in economics that captures the change in wealth needed to maintain utility at a pre-change level after a price change.

Income

Money that an individual or business receives in exchange for providing labor, producing goods, or investing capital, over a certain period.

Utility Function

A mathematical representation that translates the satisfaction or happiness a consumer gains from consuming quantities of goods and services into a numerical value.