1.1 Does the sun lie at the midpoint of the line between aphelion and perihelion?

1.2 What might this imply about the orbit of Mars?  What might it imply about the assumption(s) we made about the orbit of the Earth?

2-1.1 The length of the string: ____________________________

2-1.2 What is the eccentricity of the ellipse you drew on the cardboard?

2-1.3 What happens when the eccentricity is equal to zero?

2-1.4 What happens when the eccentricity is equal to one? (Notice that you are not allowed to set the eccentricity larger than 0.9 on the computer)

2-1.5 If the Sun lies at one focus of the ellipse, what lies at the other focus?

2-1.7 If the orbit of the Earth were as elliptical as the one showed for Kepler’s First Law, what effects on the Earth’s climate might you expect to occur?

2-2.1 At what point in its orbit does the planet travel fastest?

2-2.2 At what point is it moving most slowly?

2-2.3 Calculate the orbital velocity of the Earth at perihelion and aphelion.

2-3.2 Show that Kepler’s Third Law holds for the Earth and Venus.

2-3.3 How often does inferior conjunction occur? Give your answer in Earth months.

2-3.4 Is Venus ever found at quadrature?

Now perform the same exercise for Mars and the Earth.

2-3.6 Show that Kepler’s Third Law holds for Earth and Mars.

2-3.7 How often does the opposition of Mars occur?

2-3.8 What are the minimum and maximum distances from the Earth to Mars? Give your answers astronomical units:

Mars to Earth	A.U.
maximum distance
minimum distance

2-3.9 What is the elongation angle of a planet when it is at Opposition?  When it is at Conjunction?

2-3.10 Measure the synodic and sidereal period of Mars (hint: you can do this without using a protractor.  think about the last question you answered.).

	Years
synodic period
sidereal period

2-3.11 Is Mars ever found at quadrature?

2-3.12 Which planet (in the solar system as a whole, not just this model) moves the largest number of degrees per day in its orbit around the Sun?

2-3.13 Which moves the least?

3.1 In what constellation is Mercury now?

        date: _______________ constellation: _____________________

3.2 What is the maximum elongation angle of Mercury? ___________ degrees

3.3 When is Mercury at superior conjunction? __________________

3.4 When is Mercury at inferior conjunction? __________________

3.5 In what constellation is Venus now? ___________________

3.6 What is the maximum elongation angle of Venus? ___________ degrees

3.7 Is Venus at inferior or superior conjunction and when? _______________

3.8 In what constellation is Mars now? ___________________

3.9 When will Mars be at the next opposition and conjunction? __________________

3.10 Does Mars show retrograde motion in 2009? ______________ When? ____________

3.11 Imagine that you were an observer on Mars. In what constellation would the Earth appear on April 1, 2009?

3.12 Imagine that you were an observer on Mars. In what constellation would the Sun appear on April 1, 2009?

3.13 In what constellation is Jupiter now? ________________

3.14 When is Jupiter at conjunction? ________________

3.15 Will Jupiter exhibit retrograde motion in 2009? ___________ When? ___________

3.16 In what constellation is Saturn now? ___________________

3.17 When is Saturn at opposition? ________________________

3.18 Imagine that you were an observer on the Sun. In what constellation would the Earth appear on January 1, 2009?

            July 1, 2009?