The options for the first two are heliocentric, geocentric, or retrograde

the options for the last one are faster, slower, or larger

The loops in Ptolemy's geocentric model, and those shown on the video, are called retrograde motion.

This phenomenon is caused by the Earth's larger orbit than those of other planets.

Ptolemy's model is called geocentric because it puts Earth in the middle of the solar system, and the whole universe in fact. Geo means "earth," and centric means "at the center."

Ptolemy believed that the other planets orbited in a circle (the epicycle) whose center point itself orbited in a circle (the deferent) around the Earth. That would explain why sometimes the planets are observed as going backwards (i.e. in a retrograde motion) when seen from the Earth: half of a planet's epicycle runs in the opposite direction to that of the deferent path. The combined motion therefore appears slower or backwards.

The Earth does not have any orbit in Ptolemy's model; it is stationary while everything else rotates around it. So the answer in the last sentence is probably "larger," by elimination, because an orbit cannot be "fast" or "slow" since it's a trajectory.

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