Distance of the Stars

The Easiest Constellation

Orion is an easy constellation because you can spot it so quickly by his belt in the sky. Let's do some calculations to see how far apart the stars are on the diagram below.

Orion

The Farthest Apart

Based on the diagram above, which two stars seem the farthest apart?

Drawing it out

On the diagram above, create a segment connecting the two points you gave as your answer for the previous question. Then make a right triangle using that segment as the hypothesis and compute the distance between the two stars using the Pythagorean Theorem. Put the values you used for a and b, then put the final value you obtained for the distance between the two stars below. (Note: you can guesstimate the lengths of a and b, you don't need to get exact answers.)

The Closest Together

Now choose which two points you believe are the closest together on the diagram above and notate them below. Put a segment to connect the two points and create a right triangle just as you did in the previous question. Tell me the a and b you used and then tell me the distance you got for those two closest stars.

Is it real?

Look at your answers for the farthest stars and the closest stars. Do you think those are actually the closest and farthest from each other in the real-life version of the Orion Constellation? Or is it possible we're completely off? Explain your reasoning.

The 3D Distance of the Stars

Of course, stars are spread out through space at many different distances from our own Sun and from each other. They are not all on the same plane, despite how they look to us in the sky. In this problem, you will calculate the distances between some familiar stars using the 3-dimensional distance formula in Cartesian coordinates. Our own Sun is at the origin of this coordinate system, and all distances are given in lightyears. The distance formula is given by:

The origin of the formula

Where do you think this formula comes from?

Select all that apply

A
Triangle Sum Theorem
B
Pythagorean Theorem
C
Godel's Incompleteness Theorem
D
Vertical Angles Theorem

Check my answer (3)

The coordinates for each of the stars we are working with is shown below along with a star map. Feel free to move the star map around to see all the stars. You can also zoom in.

Far away solar systems

Which star do you think is the farthest away from the sun? There are two possible contenders.

Calculations

For the star that you think is the farthest away, calculate the distance and input that here.

Checking your answer

Let's see if you're right. Check the other contender and input that distance here.