Chapter Questions
If we discover a new planet in the Solar System and observe that it takes about one Earth year between oppositions, what could we say about it?
If you lived on Mars, what would the greatest elongation of the Earth be?
When Mars is in conjunction, within an angle of about $5^{\circ}$ of the Sun, we lose radio contact with our spacecraft there. Based on the synodic period of Mars, estimate approximately how long this period of communication problems lasts.
Make a geometric construction (or use trigonometry) to show that Venus's orbit is about 0.72 times the size of Earth's, based on the fact that Venus's greatest elongation is $47^{\circ}$.
Redraw Figure 11.7 to show that retrograde motion can also be seen for a planet closer to the Sun than the Earth. Near what position would we expect to see retrograde motion for such a planet? What would an observer on this planet see of the Earth's motion?
Mars spends, on average, about $11.5 \%$ of its orbit moving from opposition to quadrature. Make a geometric construction (or use trigonometry $)$ to show that Mars's orbit is about 1.52 times the size of Earth's.