Our Galaxy presents mankind with a new scientific frontier, expressed in different ways. In astronomical terms, it is not clear how the galaxy exists and operates as a single, unified system. In terms of the Earth's history, we see records of dramatic climate changes, variations in geophysical activity, and even fluctuations in the evolutionary process of life all corresponding to the changing relationship of our Solar System with the Galaxy. While these are often presented as independent studies, the 2015 Basement research report “Towards a Galactic Science Driver” examines these as aspects of a single challenge: the quest to understand the unifying principle of our Galaxy, as Kepler had discovered the unifying principle of our Solar System.
In a continuation of this effort, here we will examine what we know (and what we don't know) about the motion of our Solar System through the Galaxy. This will be addressed in a series of posts.
Part 1 will examine our ability to make direct measurements of the distance and motion of other stars.
This will be the basis for measuring the motion of our Sun against large groups of surrounding stars, as will be covered in the second post. After that we can examine the spiral arm structure of our galaxy, and our Solar System's motion relative to large scale galactic structures.
We tend to think of the stars as having fixed positions in the night sky. Over weeks and months we observe the planets moving through various constellations, the Sun will rise and set against different stars, and the Moon migrates through the zodiac. All the while the stars keep their same position to each other – or so it might seem.
Figure 1 – Mars' motion relative to the “fixed” stars over the course of eight months. This image was NASA's Astronomy Picture of the Day for May 11, 2008, Credit & Copyright: Tunç Tezel (TWAN)
The accuracy with which astronomers can measure positions in the sky has improved to such a degree that astronomers can directly measure incredibly small changes in the positions of stars.
This was first achieved in the 19th century (for the closest stars), and with today's satellites we can measure the motion of millions of stars (with a billion stellar motions to be precisely recorded in the coming years).
This increased capability is directly tied to the precision of instrumentation.
In the time of Johannes Kepler (before the use of telescopes), the positions of stars (and planets) could be measured with a precision determined by the limits of the unaided human eye – a few arc-minutes (there are 60 arc-minutes in one degree).
Figure 2 – The angular size of different astronomical objects, compared with the angular size of a letter from an eye exam (corresponding to 20/20 vision). For each of the astronomical objects the largest angular size is given. Angles are measured in arc minutes (denoted by a single prime symbol ( ′ ), looking similar to an apostrophe), or in arcseconds (denoted by a double prime symbol ( ′′ ), looking similar to a quotation mark). An arcminute is one sixtieth of a degree, and an arcsecond is one sixtieth of an arcminute. The graphic adapted from an original by the Wikipedia user Cmglee, and is licensed as Creative Commons Attribution-Share Alike 3.0 Unported.
To work with these measurements a coordinate system is agreed upon, and the angular position (latitude and longitude) of stars (or planets) are measured relative to that chosen reference system. Kepler, for example, could measure a star's (or planet's) position by degrees along the celestial equator (the projection of the Earth's equator onto the celestial sphere) and degrees above or below the celestial equator (towards or away from the North Star). With these two measurements, referred to as right ascension and declination, any position on the sky could be determined, recorded, and communicated. (For more on Kepler's creation of true physical astronomy, see the excellent pedagogical website dedicated to Kepler's New Astronomy).
Figure 3 – A depiction of a right ascension and declination coordinate system on the celestial sphere. The graphic was produced by the Wikipedia user Tfr000, and is licensed as Creative Commons Attribution-Share Alike 3.0 Unported.
With the development of telescopes came increasing precision, enabling the position of planets and stars to be recorded with increasing accuracy. Today space telescopes are often the best, getting above the visually-noisy atmosphere.
In 1989 the European Space Agency launched the Hipparcos satellite, whose sole mission was to spend four years precisely measuring the angular positions of millions of stars. Hipparcos could determine the position of a star with a precision 60,000 times better than the unaided human eye – about 0.001 arc-seconds, a precision of one 3.6 millionth of one degree.
To use a familiar example, the north star, Polaris, is not exactly at the north pole of the celestial sphere. With the precision of the human eye, it can be determined to be 0.74 degrees (or 44 arcminutes) away from the precise location of the pole. With the precision available with the Hipparcos it can be measured more accurately, at 0.735891 degrees (or 44 arcminutes and 9.208 arcseconds) away from the precise location of the pole.
Figure 4 – A picture of a technician examining the Hipparcos satellite before its launch in 1989. Picture credit: Michael Perryman; Creative Commons Attribution-Share Alike 3.0 Unported.
With this precision we can clearly see that the relative positions of stars are not fixed, but change over time. This is detected by measuring the precise position of a star, then come back at a later time and precisely measure the position of that same star again to see if its position changed over the intervening time. If a change in position is detected there are two different causes of the observed motion (somewhat similar to the first and second inequalities Kepler addresses in his New Astronomy).
First, we can observe stars appearing to move because we are observing from a moving position – our Earth's orbit around the Sun. This parallax effect can be very useful. If we measure the position of a star once, and then measure the position of that same star again six months later, we know exactly how the location from which we are making that observation has changed – we're on the opposite side of the Earth's orbit (two astronomical units away). This creates a parallax effect, which can be used to directly measure the distance of that star. This was first done by Friedrich Bessel in 1838, when he measured the star 61 Cygni to be 10.3 light years away (equivalent to 651,400 AU, or 9.745*10^13 km).
Figure 5 – An illustration of how a relatively nearby star will appear to change its observed position (as seen against farther stars) when the Earth is viewing it from a different side of its orbit around the Sun. This parallax effect can be used to measure the distance of that star. The graphic was produced by the Wikipedia user WikiStefan, and is licensed as Creative Commons Attribution-Share Alike 3.0 Unported.
With the precision of the Hipparcos satellite, distances could be measured for stars up to 1,600 light-years away (if they are bright enough) – one percent of the estimated diameter of the Milky Way, putting many stars within reach.
In 2013 the European Space Agency launched a successor mission, Gaia, which will far surpass the achievements of Hipparcos (the final results from the Gaia mission are expected in 2020, with partial results released along the way). Gaia's precision is 100 times greater than Hipparcos (measuring with an accuracy of 0.00001 arcseconds, compared to Hipparcos' 0.001), enabling the accurate detection of even smaller parallaxes, corresponding to distances of up to 30,000 light years (encompassing a significant portion of our entire galaxy!).
Figure 6 – A visualization of the stellar distances which will be measurable by Gaia, including a comparison with the distances measurable by Hipparcos.
We also need to consider a second type of motion, that attributed to the actual motion of the stars through space (rather than the motion of the Earth around the Sun). If we measure a star once, and then measure it again some whole number of years later we can't attribute any change in position to parallax (because the Earth is in the same position in its orbit around the Sun), and we must conclude that any observed change is due to the relative motion between our Sun and that star. This is referred to as “proper motion.”
Figure 7 – An illustration of the hypothetical proper motion of a relatively close star (with measurements one, two, and three years apart), measured against more distant stars and galaxies. For comparison, one measurement from six months after the first measurement is shown, displaying the effect of parallax.
As would be expected, some of the closest stars to us have the largest proper motions, and their proper motions have been measurable for many decades now. For example Barnard's star has the largest proper motion of any star, moving at 10.3 arcseconds per year (recall that Hipparcos and Gaia measure in thousandths and hundreds of thousandths of arcseconds). It's proper motion was measured by Edward Bernard in 1916.
Figure 8 – Barnard's Star imaged between 1985 and 2005. Credit: Steve Quirk.
The precision of the Hipparcos satellite has placed millions of stars within reach of these two measurements (with 100,000 of these stars measured with very high precision; 2.5 million measured at a lower precision). When in operation (1989-1993) Hipparcos measured the positions of each star multiple times a year over the course of four years. The resulting observed motions are a combination of these two effects, parallax (due to the Earth's orbit) and the proper motion (due to the motion of the observed star, relative to the Sun).
Parallax and Proper Motion Combined
The ESA has provided a website which allows anyone to display the observed motion of any star in the Hipparcos catalog.
Some stars have relatively comparable values for their parallax and proper motion, displaying a nice clear series of loops across the sky – as is seen with the star Ross 675 (HIP 54).
Figure 9 – The observed motion of star Ross 675 (HIP 54) over four years of observation by Hipparcos. Right ascension (RA) and declination (Dec) values are measured in milliarcseconds (mas). The pink line is how Ross 675 would appear to move if viewed from the center of our Solar System (rather than from the Earth), removing the effect of parallax.
Other stars have proper motions so much greater than their parallax that they only display a small wiggle as they traverse the sky – like Kapteyn's Star (HIP24186).
Figure 10 – The observed motion of star Kapteyn's Star (HIP24186) over four years of observation by Hipparcos.
While others have the opposite, very little proper motions (relative to their parallax), resulting in a pattern dominated almost fully by parallax – as is the case for the star Gliese 710 (HIP89825).
Figure 11 – The observed motion of star Gliese 710 (HIP89825) over four years of observation by Hipparcos.
From Angular Motion to Space Velocity
In each of these three examples we're examining angular motion as seen on the “celestial sphere” without considering actual distances and speeds. Using the parallax measurement we can set a distance to that sphere, allowing us to convert the apparent motion across the sphere to a speed (measured in kilometers per second). This doesn't yet give us the speed of the star's actual motion through space, but how fast the star would be moving if it were moving along a spherical surface at that distance (what is called the transverse (or tangential) velocity).
With the addition of one more type of measurement we can determine the actual motion of the star through space (relative to our Sun).
We can measure how fast a star appears to be moving either directly towards us or directly away from us (what is called the radial velocity) from the Doppler shifts in the spectral features of the star's light (red or blue shift).
By combining this radial velocity with the transverse velocity, we can get the actual motion of the star through space (relative to our star) – what is called the “space velocity”).
Figure 12 – The combination of the transverse velocity (along the sphere; from position “A” to “B”) with the radial velocity (directly away from or towards us; from position “B” to “C”) gives us the motion of the star through space (relative to our own star; from position “A” to “C”).
From these measurements we can directly measure how far away a star is, how fast it is moving, and in what direction – all relative to our own Sun. All together six values are needed for this determination.
Two measurements to determine an initial position on the celestial sphere:
• Longitude (right ascension, or galactic longitude, or some other determination)
• Latitude (declination, or galactic latitude, or some other determination)
Two measurements of the proper motion along the celestial sphere:
• Proper motion in longitude
• Proper motion in latitude
One measurement to determine distance:
One measurement to determine radial velocity:
• Doppler shift
Let's examine how to work with these six parameters using a specific example.
Star Gliese 710
Above we saw the Hipparcos plot for the star Gliese 710. Its position was at 274.96183965º (274º 57' 42.623'') right ascension and -1.93861165º (-1º 56' 19.002'') declination.
Hipparcos measured its proper motion at +1.74 milliarcseconds per year in the direction of right ascension, and +2.06 milliarcseconds per year in the direction of declination – for a total proper motion of 2.7 milliarcseconds per year.
Figure 13 – An illustration of the position of Gliese 710 on the celestial sphere (right ascension and declination) and the proper motion of Gliese 710.
Hipparcos measured a parallax of 51.81 milliarcseconds, placing Gliese 710 at a distance of 64 light years (4,047,000 AU, or 6.055*10^14 km).
With this we can say that if Gliese 710 were moving on a sphere of radius 64 light years it would be moving along the spherical surface at 0.25 kilometer per second (the transverse velocity).
Figure 14 – The distance and proper motion of Gliese 710 allows us to calculate a transverse velocity of 0.25 kilometers per second (traveling 7,930,000 km in a year).
We can now include a separate measurement of the radial velocity, -13.8 kilometers per second (from a Doppler shift of z=0.000046), which tells us that over the course of one year Gliese will travel 435,196,000 kilometers (0.000046 light years) towards our Sun.
Combining this radial velocity with the transverse velocity tells us that Gliese 710 is traveling through space (relative to our Sun) at 13.802 kilometers per second.
Figure 15 – The transverse velocity and radial velocity of Gliese 710 allows us to calculate its space velocity at -13.802 kilometers per second.
Because Gliese 710 has a very low proper motion and a negative radial velocity we know that it is heading nearly directly towards us.
At its distance of 64 light years and a speed of 13.8 kilometers per second, Gliese 710 will pass closest to our Sun in 1.4 million years.
By our values given here it will pass the Sun at a distance of 1.2 light years, or 74,000 AU (2,500 times the orbit of Neptune). However, there are error ranges in these values, and it is possible that our incoming neighbor will pass by closer (or farther). Some have calculated a low chance of Gliese 710 perturbing comets in the Oort cloud (1,000 to 100,000 AU) enough send some of them into the inner Solar System.
However is it extremely unlikely to have any gravitational effect on the planetary orbits of our Solar System, or on the Sun's path through the galaxy.
To conceptualize why this is the case we can make a comparison. If the Sun were the size of a single grain of salt (0.3 mm in diameter) Neptune's orbit around the Sun would be two meters away from the Sun. Gliese 710 (also the size of a single grain of salt) would be an astounding 230 kilometers away from the Sun! Even if they seem to be perfectly lined up, it is easy to see the chances of one grain of salt hitting another grain of salt (or even coming close) from a distance of 230 km is incredibly low.
In general the chances of a Sun-star pairwise gravitational interaction (let alone impact) is exceedingly small for these reasons.
For Next Time
Our examination of the star Gliese 710 is just one example. Between the work of Hipparcos and additional surveys (for radial velocity), thousands upon thousands of stars have been measured in this way, telling us how far away they are and how they are moving relative to our own Sun.
With large samples of various stellar motions we can begin to measure how our Sun is moving relative to large groups of stars, and begin to estimate how our Sun is moving with respect to the Milky Way Galaxy itself.