Do Constellations Look Different on Other Planets? ⭐️
No. See you next week...Just kidding!
But we can use some math and basic principles of triangles to prove that: if you were standing on the surface of another planet in our solar system that the stars would still sit in the same position and form the same familiar constellations in the night sky
Ok, let's set up this problem in a way we can solve it. First, fundamentally, how are we going to determine if a star's position in the night sky changes? First off, how do we determine what a star's positions is in our night sky?
Normally when you measure something you might think to use a ruler. But standing on the surface of Earth and looking up at Sirius or Polaris, a ruler wouldn't give us a number that means anything. Instead, we can measure a star's position as an angle.
For example, the Northern Star (Polaris) gets it name because in the northern hemisphere of Earth, it sit at (essentially) the north celestial pole. So, throughout the night stars will rotate around as the Earth rotates along its axis, but Polaris will remain stuck in place since it sits on the same axis that the Earth is rotating on.
Polaris is special because of how close it sits to the north celestial pole, which means that the angular distance from the horizon to Polaris only varies based on your position on Earth. Closer to the top Earth like the North Pole, Polaris will appear directly above, but at the equator will rest low on the horizon. In places like Boston or Greenwich, it will sit roughly halfway up. You can use Polaris to determine your own latitude because of this!
Your latitude is simple the angular distance from the horizon to Polaris. In Greenwich, Polaris is 52° above the horizon and Greenwich's latitude is, low-and-behold, 52°.
While this math will work for any star, we will use Polaris for now since its position only depends on latitude. Other stars, like Sirius need a position, time, and day of the year to determine their position.
Ok, let's use some triangles!
So, we can represent the position of Earth and a planet (let's say Jupiter) as the two bottom vertices since they lie roughly in line with each other. The top third vertices will represent the star Polaris.
We can start labeling sides and angles and you will see why turning this problem into a triangle makes it simple to solve.
For the purpose of this problem, let's say that we are sitting in Greenwich, so angle "a" will be 52°. The purpose of this problem is to solve for angle "b" since that will tell us what the angular position of Polaris is on Jupiter. Angle "c" will represent what the angular distance between Earth and Neptune would be if you were standing on Polaris (and not burning to death). At a glance, we can guess that angle "c" will probably be pretty small since we can't see planets rotating around other planets with the naked eye from Earth.
But let's keep the triangle more general to make this easier to visualize. The sides of the triangle are next.
Side "x" is the easiest, since that is just the distance between Earth to Jupiter. This can vary a bit since orbits are not perfect circles, so there is a time of year when Earth is closer to Jupiter (perhlihion) and when it is farther (aphelion). To be generous, let's use aphelion.
Side "y" is also simple, this is the distance between Earth and Polaris. We will keep all these distances in light years.
Side "z" is a little harder to visualize with this more general triangle, but that would represent the distance from Jupiter to Polaris.
The Law of Sines is a feature of triangles that states that there is a relationship between the sides of a triangle and its angles:
Alright, time for triangle math. So what we know we have is:
Side "x" = 4.799 x 10^-4 light years (aphelion) from Earth to Jupiter
Side "y" = 433 light years to Polaris from Earth
And...that's kind of it right now. We can make some rough estimates for side "z" as the distance to Polaris to but let's start with we know we have: two sides and one angle.
We can plug in those numbers now:
Well, that is an awfully small angle. If we were to draw that as a triangle, it would probably look more like a straight line.
With angle "c", we can finally solve for the angle we need since all the internal angles of a triangle will add up 180, so we can say that angle "b" is:
But, what we need is actually the opposing angle for "b", which we will call "b' "
Hey, look at that, we did it!
On Earth (in Greenwich), Polaris sits at 52°, and now we know that on Jupiter it would 52.000008998°. Typically, the human eye can only see about 0.017 (1/60th of a degree) differences in degrees so the difference on Jupiter would far too small to make out at about 9 millionth of a degree.
And, now we have a general equation to be able to use for any star, at any latitude on Earth, and for any position:
Let's try this out with a Neptune, Sirius, and in Boston.
Sirius is a little trickier than Polaris since its position in the sky changes through the night, but on January 5, 2025 at 2:44 AM in Boston, the position is at 15.81°
Side "x" = distance from Earth to Neptune (aphelion) = 4.5 billion km = 4.799x10^-4 light year
Side "y" = distance from Earth to to Sirius = 8.6 light years
Sirius would have a difference in position of about 870 millionths of a degree, which is more than we saw on Jupiter but still too small to see with the naked eye.
💫 The moral of this story: the secret to most problems in the world is to find a way to turn the problem into a triangle 💫
