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Problems

1

Suppose an inferior planet has a sidereal period of 0.6 years. Find the synodic period of the planet. What would be the synodic period of the Earth when observed from the planet?

2

What is the sidereal period of a planet that has a synodic period of 0.7 years?

3

Suppose a superior planet has a sidereal period of 1.4 years. What would be the synodic period of the planet?

4

What are the possible sidereal periods of a planet that has a synodic period of 1.5 years?

5

What is the synodic period of Saturn when observed from Jupiter?

6

What is the synodic period of Mercury when viewed from Venus?

7

A hypothetical planet is 70° from the Sun at greatest elongation. Draw the triangle showing the positions of the Sun, planet, and Earth at greatest elongation. Using the triangle, find the distance of the planet from the Sun in AU.

8

When viewed from Mars, what is the angle between the Earth and the Sun when Earth is at greatest elongation?

9

Use the small angle equation to confirm Tycho's conclusion that if a star had an angular diameter of 1 minute of arc and a distance of 7000 AU it would be much larger than the Sun.

10

Draw an ellipse for which the distance between the foci is 10 cm and the length of the major axis is 20 cm. What is the eccentricity of the ellipse? If a planet orbits on the ellipse, what is its perihelion distance? What is its aphelion distance?

11

How far apart are the foci for an ellipse that has a major axis of 10 cm and an eccentricity of 0.0?

12

Pluto has an orbital eccentricity of 0.25. Find the perihelion and aphelion distances of Pluto. What is the ratio of Pluto's orbital speed at perihelion to that at aphelion?

13

What is the sidereal period of a hypothetical planet with an orbital semimajor axis of 0.7 AU?

14

What is the sidereal period of a hypothetical planet with an orbital semimajor axis of 3.5 AU?

15

What is the orbital semimajor axis of a hypothetical planet with a sidereal period of 0.7 years?

16

What is the orbital semimajor axis of a hypothetical planet with a sidereal period of 25 years?

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