Brain Teasers about astronomy

The following questions about the earth, moon, and sun all have simple solutions that can be constructed without any advanced technology.  Just careful reasoning, cleverness and creativity.

How would you determine ...
  1. The shape of the earth.
  2. The size of the earth (circumference).
  3. The shape of the moon.
  4. Whether the earth goes around the sun, or vice versa.
  5. The relative distance of the sun and moon.
  6. The relative sizes of the sun, earth, and moon.
  7. Whether the earth spins under the heavens or vice versa.

1.  Eclipses occur at varying times, yet the shadow is always a circle.  The shadow of the earth on the moon during a lunar eclipse was always circular. The only shape that always casts a circular shadow is a sphere.
2.  Eratosthene's heard there was a place where at midsummer's day the sun could be seen at the bottom of a well.  So he knew the sun would be directly overhead.  So on this day at noon he measured the angle of the shadow cast by a vertical pole in Alexandria (500 miles north of the well.)  The angle was measured at 7 degrees, so he knew that 500 miles was 1/51 of a circle, and was able to estimate the circumference.
3. The moon isn't a disk else we would see all light or all dark.  Phases of moon can only be caused by a sphere.
4. We must simply go outside every night for a year. At first the stars will look like a jumbled mass, but as we get more familiar with them, certain patterns become clear. Over a few months, the patterns will slide sideways, disappearing over the edge of the horizon. At six months, the original patterns will be completely out of view. Then, over the next few months, they will turn back into view, and at the one year mark they will return to their original configuration.
By keeping a careful record of the stars at night, including their proximity to each other, we are able to see apparent shifts in star position over time. These shifts in star position, paradoxically enough, prove that universe around us is (relatively) stationary, and we are the ones moving.
5.At first quarter, the angle from the moon to the sun is 90 degrees.  So using a piece of paper he measured the angle from earth to sun and calculated the ratio of angles.  His crude calculations were a ratio of 1 to 11.  Modern measures are 1 to 400.  (details).
6. Sun and moon have same apparent diameter, so since the sun is 11 times farther away, it was 11 times larger.
7. Foucault Pendulum