My neighbor watched the conjunction of Mars and the Moon last Sunday evening. On the beach the next day he was trying to get a feel for the 3-D relationship. Here's what I had to say.
First, since the Moon was full, it was on the opposite side of the Earth from the Sun. Since Mars was in the same part of the sky, it too was opposite the Earth from the Sun -- and therefore as close to the Earth as it gets on our mutually concentric orbits. So imagine the Earth, Moon and Mars strung out in a line from the Sun.
How far the Moon? Wrap a string around the Earth's equator 10 times. Now unwind it like a yo-yo string. That's the distance to the Moon. Wrap the string around the Earth 2,000 times. That's the distance to Mars. Last Sunday night, Mars was 200 times farther away than the Moon.
Here's another way to think about it. Imagine the Earth is a basketball. The Moon would be a tennis ball about 25 feet away -- from one side of a big room to the other. Mars would be a softball a mile away. (I drew the circles in the sand, and pointed to the imaginary softball way down there at the far end of our mile-long beach.)
So there we were on Sunday night, standing on the night side of the basketball, looking at the fully-lit tennis ball 25 feet away -- like a big eye in the sky -- and almost touching it in our line of sight, the red glow of the fully-lit softball a mile away.
Those tiny objects in all that vastness of empty space. (Wrap the basketball in Saran Wrap and that thin film is sufficient to represent the atmosphere.)
The Sun invisible behind us, two miles away from our basketball Earth -- way down there at Farmer's Hill communication tower in the opposite direction along the shore -- a great blazing ball as big as the tower is tall.
And all of this is just an miniscule speck in the almost unimaginable vastness of the galaxy, itself a dust mote in the cosmos.