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Problems

1

The synodic period of Jupiter is 399 days. What is the interval of time between successive times that Jupiter appears in opposition at the same position among the stars? (This problem will have to be done by trial and error.)

2

What is the angular diameter of an object that has a linear diameter of 30 meters and a distance of 1000 meters?

3

What is the distance of an object that has an angular diameter of 100 seconds of arc and a linear diameter of 30 meters?

4

What is the linear diameter of an object that has an angular diameter of 20 seconds of arc and a distance of 50,000 meters?

5

Suppose the distance to an object is tripled. What happens to its angular diameter?

6

Planets A and B have the same angular diameter. Planet A has a linear diameter that is 25% larger than that of planet B. What is the ratio of the distance of planet A to the distance of planet B?

7

Suppose the angle between the Sun and Moon (as viewed from the Earth) at quarter moon is 75°. Use a protractor to find the ratio of the distances to the Sun and Moon using the method of Aristarchus.

8

Suppose Eratosthenes had found that the difference in the altitude of the Sun at Syene and Alexandria was 15°. What value would he have found for the resulting circumference of the Earth?

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