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Proper motion

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Proper motion is an astrometric measure of how a celestial object moves across the sky. It tracks the change in an object's angular position over time. This measurement is taken relative to the center of mass of our Solar System. Astronomers use distant stars or a stable reference called the International Celestial Reference Frame (ICRF) as a baseline. While stars appear to stay in fixed constellations, they are actually moving independently. Over very long periods, these motions cause the shapes of constellations to change.

Proper motion
Proper motion

To calculate this motion, scientists look at two specific directions in the sky. These directions are right ascension, which measures east-west position, and declination, which measures north-south position. Proper motion is a two-dimensional vector. This means it includes both a magnitude and a position angle. The magnitude is the speed of the angular change. This is typically measured in arcseconds per year or milliarcseconds per year. The position angle tells us the direction of the motion on the celestial sphere.

Proper motion
Proper motion

Measuring these movements requires precise math to account for how we view the sky. When an object moves from one set of coordinates to another, we calculate its change in right ascension and declination. Because the lines of right ascension widen as they move toward the celestial poles, a correction factor is needed. This factor uses the cosine of the declination to ensure the math remains accurate. Scientists often use a converted value called the proper motion in right ascension, or $\mu_{\alpha}^*$, to make calculations straightforward. This process allows researchers to find the total proper motion, $\mu$, using the Pythagorean theorem.

Most stars have very small and unremarkable proper motions. Many are so distant that their movement is less than 0.01 arcseconds per year. However, stars with high proper motion are often much closer to our Sun. For example, Barnard's Star has the largest proper motion of any star at 10.3 arcseconds per year. It is a red dwarf located about 6 light-years away. Another notable example is 61 Cygni A, which has a proper motion of 5.281 arcseconds per year. In 1992, the star Rho Aquilae moved so much that its Bayer designation was invalidated. It actually moved from one constellation into a neighboring one, Delphinus.

Barnard2005
Barnard2005

Understanding proper motion is vital for calculating a star's true space motion. Proper motion only shows movement across the sky, not movement toward or away from us. To find the true velocity, astronomers must combine proper motion with radial velocity, which is the speed along the line of sight. They also need to know the distance to the star. A proper motion of 1 arcsecond per year at a distance of 1 light-year equals a transverse speed of 1.45 km/s. For Barnard's Star, combining its proper motion with its radial velocity reveals a true space motion of 142 km/s.

Proper motion
Proper motion

History shows that humans have long wondered about the movement of the heavens. While some suspected movement as early as AD 400, proof did not arrive until 1718. The astronomer Edmond Halley provided this proof by comparing modern star positions to ancient charts. He studied the work of the Greek astronomer Hipparchus, who lived about 1,850 years before Halley. Halley noticed that stars like Sirius, Arcturus, and Aldebaran were more than half a degree away from where Hipparchus had recorded them. This confirmed that stars do indeed move through space.

Today, studying these motions helps us understand the structure of the entire universe. Patterns in proper motion can reveal stellar streams or the rotation of the Milky Way disk. It can even help us weigh objects. By measuring the motion of stars in a globular cluster, scientists can use the Leonard-Merritt mass estimator to find the cluster's total mass. Proper motion also helped confirm the existence of Sgr A*, a super-massive black hole at our galaxy's center. This black hole has a mass of 4.3 times that of our Sun.

Proper motion
Proper motion

Proper motion is also a tool for measuring the scale of the cosmos. It can be used to estimate the distance to objects in the Local Group of galaxies. In 1999, scientists measured the rapid motion of water masers to find the distance to the galaxy NGC 4258. In 2005, the first proper motion measurement was made for the Triangulum Galaxy, M33. Astronomers even used these measurements to track the Andromeda Galaxy. They have predicted that Andromeda will collide with the Milky Way in about 4.5 billion years.

Barnard2005
Barnard2005
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