Ancient observations

If you look at Mars in the night sky over time, you’ll notice that Mars gradually grows and shrinks in size over the course of two years.

This observed change is due to the orbital positions of Earth and Mars over time, and the shapes of Earth’s (nearly circular) and Mars’ (more elliptical) orbits. The following animations shows how the distance changes over time. Notice how they are closest anytime they form a straight line with the sun (animation not to scale):

Depending on its orbital position and Earth’s atmospheric conditions (and, today, the amount of light pollution), Mars may or may not be visible to the naked eye. As a general guide, people can see objects about 1 arcminute without telescopes or other magnifying aids.  In the 5th Century C.E., an Indian astronomical text by an unknown author estimated the angular size of Mars as 1/30 of a degree (or 2 arcminutes). This measurement was a slight overestimate compared to the actual values known today:

The text also calculated the distance between Earth and Mars as 10,433,000 km. This measurement was an underestimate, as we now know that the actual value ranges as follows:

Using the 5th Century C.E distance and angular size, the author applied basic geometry to estimate the diameter of Mars. Using these values, the diameter of Mars came out to 6,070 km. Impressively, this estimate was only 11% off of the actual values we know today: 6779 km.

Challenge Question: Next we wanted to determine the length of a year and day on Mars. What data would you need to determine this?