At dinner last night the topic of sending humans to Mars came up. I don’t remember how or why – we just started talking about it and my younger son was really interested. When I asked the boys if there was anything they wanted to talk about for our project this morning the topic was Mars.

The tiny little problem with this topic is that I know absolutely nothing about it! But with a little prep work this morning I was able to throw together what was hopefully a fun 30 min.

We started by watching this short video:

After the video we talked about a few of the ideas. I almost went down the rabbit hole of explaining a bit of mechanics, but probably luckily changed my mind right before jumping in to that topic.

The next topic was Kepler’s 3rd Law. This Law says (oversimplifying) that for planets orbiting the Sun, the time of the orbit squared divided by the radius cubed is constant.

I introduced the law and did the computations for Earth and Mars.

Finally, since my older son is just starting to study trig, I wanted to show a really neat curve. I forget where I saw this idea previously, but it is a fun picture and also a neat trig example.

The question is, if we plot the midpoint of the line connecting the Earth and Mars as they orbit the sun, what does the curve look like?

This was a fun project and is also definitely a neat trig example. For a great history lesson of how humans learned more about Mars check out Terry Tao’s incredible public lecture – “The Cosmic Distance Ladder” (he’s talking about Mars around 58:00 – though maybe earlier, too):