The movement of the stars

I've been asked why the constellations we see every night are the same if the Earth is going around the sun at 66,000 mph and if the sun is going around the galaxy at close to 500,000 mph. How can the shape of the Big Dipper, for example, be so fixed if the sun (and other stars) are moving at such speeds?

For the impatient, here's the short answer. The movement of the stars may be "fast" by human standards, but the stars are also extremely far apart. The distance travelled by a star, even over the course of a century, is minuscule compared to the distances separating the star from its neighbors. Over the extremely brief span of a human life, our naked eyes will see the stars as "fixed."

A trip to the planet Pfizdion

If you live in the Northern Hemisphere, you are probably familiar with the above constellation, the Big Dipper. At least it looks like a dipper from our viewpoint. Let's take a journey to Pfizdion, a hypothetical planet. By playing the video below we can see how the appearance of the constellation would change during our flight.

How the Big Dipper changes as we journey to a distant hypothetical planet

The inhabitants of Pfizdion see the Dipper very differently. They call the constellation Fzenkle, named after a one-eyed pet on their planet. It is quite popular there because it sucks dust off the floor, eliminating any need for vacuum cleaners. Pfizdionites also see our sun as a dim star in their night sky. If they made star atlases with constellation art, the Dipper's neighborhood might look like this:

The Big Dipper and our sun as seen from the planet Pfizdion

The five central stars of the Dipper are all about 80 light years from Earth. (A light year is the distance light travels in one year, about 6 trillion miles.) As the Phizdionite's "side view" suggests, the two "bookend" stars are farther away from Earth. Alkaid is 104 light years away and Dubhe is 124 light years away. More later on how we know this, but we are talking about almost incomprehensible distances here. And the Dipper is in our "local neighborhood" of the galaxy!

The Big Dipper's shape is gradually changing

Our sun and the other stars in our neighborhood travel together around the center of the galaxy due to the galaxy's overall rotation. So, the Earth and the Big Dipper have a common velocity in the range of 500,000 mph. But stars also move relative to each other more slowly, typically at tens of thousands of mph. From satellites such as Hipparcos and Gaia, we can measure these relative motions. Dubhe is flying away from the central five stars of the Dipper. Using the measured positions and velocities of the stars, we can project how the shape of the Big Dipper changes over the course of a million years, starting from 500,000 years in the past and ending 500,000 years in the future. Here's a video of that simulation, which also includes the North Star. Our descendants a half a million years from now would need a different name for the constellation, perhaps Happy Face.

How the Big Dipper changes over a million years

But how is the change so gradual if the stars are moving at tens of thousands of mph? Let's answer this by looking at a situation we've experienced.

A trip in a sports car

Imagine riding in a car going west at 60 mph on an Arizona highway. You see the telephone poles by the right side of the road zooming across your field of view. But mountaintops that are 60 miles away appear almost stationary.

Nearby telephone poles and distant mountains moving by as seen from a moving car

To understand why, we need to convert to angular motions. The mountain peak also moves at 60 mph across your field of view, but from 60 miles away, that's only about 1 degree per minute. You have to stare at the mountains for a long time to detect the motion. This difference in angular motion between near and distant objects is called motion parallax.

Our brains use it to get depth perception; we perceive the telephone poles to be much closer than the mountaintops by virtue of their faster angular motion. If we had a precision instrument to measure the angular motion of the mountaintops, then knowing our speed, we can use some simple geometry to deduce how far away the mountains are.

Now imagine two hypothetical stars that are 80 light years away and flying away from each other at 100,000 mph. Again, we need to convert that motion to angles. If you do the calculation, you'll find that It would take about 10,000 years for their separation in the sky to increase by 1 degree. (For reference, neighboring stars in the Big Dipper are roughly 6 degrees apart.) This motion is too gradual to be seen by the naked eye. That's why we perceive the stars as fixed relative to one another.

How do we know?

How do we know the distances to the stars? For the nearest stars, we can use motion parallax. As the Earth orbits around the sun, it changes the angles from which we view the stars. This causes the stars to appear to move, either back and forth or around a loop, once a year.

Earth circling the sun, showing changing line of sight to a star

As in our sports car ride, there will be motion parallax. Closer stars would appear to move more than more distant ones. Here's an animation of what this might look like for a patch of sky near the plane of the Earth's orbit. Bear in mind that motions here are exaggerated; even Proxima Centauri, our nearest neighbor, would move less than 1 second of arc (1/3600th of a degree).

Motion parallax of stars as seen from Earth's orbit

Unfortunately, atmospheric turbulence blurs the stars by about 1 second of arc, which severely limits the precision of ground-based parallax measurements.

In 1989, the European Space Agency launched the satellite Hipparcos, which operated for four years. Freed from the blurring effects introduced by the atmosphere, Hipparcos could track the angular positions of stars with a precision of 0.001 seconds of arc. The satellite could measure both the back-and-forth motion of a star due to the Earth's orbit and the actual motion of the star itself. This gives us both distance and angular velocity.

If you want to find out more about Hipparcos and its successor mission Gaia, I recommend this great talk by Michael Perryman.