8.3: Proper Motion

Measuring Transverse Motion

There is another type of motion stars can have that cannot be detected with the Doppler Effect. Unlike radial motion, which is along our line of sight, or toward or away from Earth, proper motion is transverse, or across our line of sight. We see it as a change in the relative positions of the stars on the celestial sphere. These changes are very slow. Even the star with the largest proper motion takes 200 years to change its position in the sky by an amount equal to the width of the full Moon, and the motions of other stars are smaller yet.

Figure \(\PageIndex{1}\) is an example of proper motion using Barnard's star. All three images were taken of the same section of the sky 10 years apart from each other. Between the images, all of the other stars are in the same positions relative to each other except for Barnard's star. In Image (a), the star is in the center of the image, taken in 1985. In Image (b) Barnard's Star has moved downward from the center of the image. In Image (c) Barnard's Star is now near the bottom of the image. The vast majority of stars do not move this quickly, which is why the constellations that were observed thousands of years ago are mostly the same today.

Figure \(\PageIndex{1}\) : Large Proper Motion. Three images of the same star field taken ten years apart in Images (a), (b), and (c) show all stars remaining fixed except Barnard's Star, which shifts position each time due to its unusually large proper motion. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{1}\).

Because the stars move so slowly, we do not notice any change in the positions of the bright stars during the course of a human lifetime. If we could live long enough, however, the changes would become obvious. Figure \(\PageIndex{2}\) demonstrates how the Big Dipper has changed and will change in the future. In the top panel, 50,000 years ago, the asterism had a strangely shaped cup because the upper right star was farther upward and toward the left. In the center panel, the asterism is as it appears today, but shows the directions that each of the stars are moving. Most of them are moving to the upper left, while the stars on the far left and right of the asterism are traveling downward and to the right. Because of this motion, in 50,000 years the left side of the handle will have a sharper bend, and the cup will be more open.

Figure \(\PageIndex{2}\) : Changes in the Big Dipper. The top, middle, and bottom panels show the Big Dipper's stars 50,000 years ago, today, and 50,000 years from now, illustrating how proper motion gradually reshapes the familiar asterism. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{2}\).

We measure the proper motion of a star in arcseconds (1/3600 of a degree) per year. That is, the measurement of proper motion tells us only by how much of an angle a star has changed its position on the celestial sphere. If two stars at different distances are moving at the same velocity perpendicular to our line of sight, the closer one will show a larger shift in its position on the celestial sphere in a year's time. As an analogy, imagine you are standing at the side of a freeway. Cars will appear to whiz past you. If you then watch the traffic from a vantage point half a mile away, the cars will move much more slowly across your field of vision. In order to convert this angular motion to a velocity, we need to know how far away the star is.

To know the true space velocity of a star, its total speed and the direction in which it is moving through space relative to the Sun, we must know its radial velocity, proper motion, and distance. Figure \(\PageIndex{3}\) includes all of the information needed to calculate the space velocity. The space velocity includes both the radial and transverse velocities. Because part of space velocity includes radial velocity, the star's distance from the Sun can change significantly. Over several hundred thousand years, these changes can be large enough to affect the apparent brightnesses of nearby stars. Today, Sirius, in the constellation Canis Major (the Big Dog) is the brightest star in the sky, but 100,000 years ago, the star Canopus in the constellation Carina (the Keel) was the brightest one. A little over 200,000 years from now, Sirius will have moved away and faded somewhat, and Vega, the bright blue star in Lyra, will take over its place of honor as the brightest star in Earth's skies.

Figure \(\PageIndex{3}\) : Space Velocity and Proper Motion. A star's total space velocity combines its radial velocity, along the line of sight, and its transverse velocity, across the sky; astronomers measure the transverse component as proper motion and convert it to a speed using the star's distance. (CC BY 4.0; Fraknoi, et al. via Openstax Astronomy 2nd ed.) Accessible description of Figure \(\PageIndex{3}\).