If the earth was not tilted, what would be the north star?

Question

What is earth tipped toward? The simple answer is Polaris. The axis (one end of it) points at Polaris, so that's what it's tipped to point at. But when we saw "toward" what do we mean? When it is tipped "toward" one thing, what is it being tipped "away from"?

If earth were not tipped then the equator would lie in the same plane as earth's orbit. Earth being tipped 23 degrees means it is tipped 23 degrees "away from" alignment with its orbit. So a 0 degree tip would be "not tipped" and a 23 degree tip is tipped 23 degrees in some direction. What direction is it tipped in? Another way to ask this would be, what would it be tipped at if it was tipped a full 90 degrees in the general direction in which it is currently tipped 23 degrees?

Imagine a coordinate system with two axes in the plane of earth's orbit and one axis perpendicular to that plane. Earth's orbit stays in the plane, and the angle that earth is tipped points to, let's say, negative X. So the line through the north pole and south pole lies in the XY plane and the earth's orbit lies in the XZ plane. I want to look at stars and be able to see those axes, so I want to know what stars they roughly point at.

A cleaner way to ask this might be, what would be the north star if earth wasn't tipped? What would be the south star? What if it was tipped 90 degrees? That gives four of the six stars I'm looking for. I'm not sure how to phrase the question for the other two. I want to call these stars "untipped north", "untipped south", "winter", "summer", "spring", and "fall" because the direction of the stars would be the same as the direction earth is from the sun during the extremes of those seasons (northern hemisphere).

[EDIT]

The plane of earth's orbit is aligned with a celestial (infinitely distant) great circle called the ecliptic. It inversely happens to also be the path through the sky that the sun takes over the course of a year. There is a latitude/longitude coordinate system where the equator is the ecliptic called "ecliptic coordinates". So the question is actually:

Using ecliptic latitude and longitude, what 6 stars are at:

• 0, 0
• 0, 90
• 0, 180
• 0, -90
• 90, 0
• -90, 0

Answer 1

It turns out that 0, 0 on ecliptic coordinates is not the "winter" direction, nor the "summer" direction. And it turns out to be a good thing. Zero longitude is defined using the "spring" direction, and this means that converting these points to another coordinate system is really easy. The earth's axis is tipped 23 degrees, but imagine the axis on which it is tipped. Thats the spring/fall axis. This means that if we tip the whole coordinate system 23 degrees, two points stay unaffected (the spring/fall points). The tipped coordinate system is called equatorial coordinates and its more useful so everything uses it. The point 0, 0 is the same in both coordinate systems, as is the antipode of 0, 0 which is 0, 180. So you can get the spring and fall stars right away by browsing something like http://www.sky-map.org/

Note that the longitude coordinates are in hours (0 to 23) instead of degrees (0 to 360), and they are shown in the order longitude, then latitude. Also note that stars you can see without a telescope have an apparent magnitude of 6 or less.

Zero longitude is the direction the sun is in when it is spring, so the 0, 0 star is actually the fall star.

Now the other four stars: because the difference between the two coordinate systems is a single rotation around the spring-fall axis, the winter/summer points actually keep their longitude the same during the rotation. And because the amount of rotation is 23 degrees:

• 0, 90 becomes 23, 90
• and 0, -90 becomes -23, -90

You can check this here: https://lambda.gsfc.nasa.gov/toolbox/tb_coordconv.cfm Note that equatorial coordinates are called "celestial" on this page. Note that you have to enter a year because the tip of the earth's axis slowly changes. Just enter the current year in both epoch boxes.

It should make sense that the untipped north star would have an equatorial latitude of 90 minus 23 degrees, and the untipped south star would have an equatorial latitude of -90 plus 23 degrees. Using the same tool to do the conversion:

• 90, 0 becomes 66, -90
• -90, 0 becomes -66, 90

If you go back to sky map and poke around in those locations, you find:

• The untipped north star is in Draco (18h 66d)
• The untipped south star is in Dorado (6h -66d)
• The fall star is in Pisces (0h 0d)
• The spring star is in Virgo (12h 0d)
• The winter/summer stars are in Gemini (6h -23d) and Sagittarius (18h 23d)

Note that the latter four stars are in zodiac constellations - this is because those constellations lie on the ecliptic.

For winter/summer which is which? Well the sun comes up in the east, so earth rotates counter clockwise, so it travels around the sun counter clockwise. We know that after the line from the sun to the earth points toward fall, it points toward winter. So whichever is left of Pisces in the sky would be the winter one:

• The winter star would be in Gemini
• The summer star would be in Sagittarius

Note that the four zodiac constellations we got are evenly spaced throughout the year, and that the months associated with them are 6 months off from the seasons we mapped them to. This is because the zodiac months are assigned based on where the sun is in the sky. You never see a zodiac's constellation at night during the month associated with it.