This is something that I worked on for years after reading in the Sky Almanac that the "Waning Half Moon seen at dawn is where the Earth will be in about three hours."
It's surprising to me now how complicated this problem seemed to be at the time.
I wouldn't even call myself an amateur astronomer but I began wondering how to figure out the direction the Earth is heading at any moment in the day (or night).
There are complicating factors. First the Earth rotates every 24 hours, so the orbital direction is constantly changing. Second, the Earth has a tilted axis so the orbital direction changes north and south through out the day. Third, because this tilt is constant, the Earth's vertical axis relative to it's orbital plane changes through out the year.
Fourth, the latitude of the observer changes the relative direction.
I thought about this on and off and then I began teaching science. We were encouraged to make our teaching 'relevant' to our students' lives. One professional development leader (probably on a career path from the English Department through Administration to Assistant Superintendent of something that sounds important) said, 'Astronomy, well do what you can.'
So I started to solve my puzzle. It was fun. To a real astronomer it would be like watching a cat figure out how to get the treat in one of those puzzle toys. I've yet to meet an astronomer who can point in the direction the Earth is traveling in its orbit 'right now'. None of the sky or star Apps has it.
I came up with a method where I wave my arms around, depending on the time of day it can look like 'dancing Hitlers on Broadway.' When I tried to teach it to my college student son, he wasn't about to rise from his slouch on my couch and do anything so ridiculous, but he did say, "You know, you could probably make a right hand rule with that."
Arrggghh! Almost immediately it was obvious. 25 years for me, ten seconds for him.
I will argue that since Copernicus it has been possible to come up with this, but no else has.
If you learn this you might say, 'yeah, neat. Great for the kids,' but for me looking at the planets in the sky they are no longer abstractions. It's clear which direction they are heading in, which ones we will pass and which ones will pass us. At dawn when I see Venus and Jupiter, I know that in a few months we will be much closer to Venus than Jupiter, but it will be already on the other side of the sun. We'll pass Jupiter and begin seeing it in the evening instead of the morning.
So take a look:
and you might find this interesting. Earth, and us on it, aren't spinning so much as we are rolling around on our orbital path around the sun. We move one Earth diameter every 7 minutes and 8.25 seconds. If we multiple this times Pi, (3.14159) = 22 minutes 25 seconds. So every 22.43 minutes we move along our orbit as much as we move in rotation every 24 hours. At midnight our net velocity is orbital speed + rotational speed. At noon our net velocity is orbital speed – rotational speed.
One of those 'teacher moments,' you know the one's they make movies about, no not the one with Samuel Jackson...the weepy ones...Sidney Poitier, Edward James Olmos. When I teach this stuff at some point, always-every time, a student will ask, "Then why don't we feel it?" Hypatia of Alexandria and Galileo asked this question, a thousand years apart. Adults don't seem to ever ask, students? at least one, and not the one you would expect.
(34 degrees north latitude is Los Angeles)
Enjoy the ride.
All diagrams ©2009, 2016 W.Nettles
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