The Astrogators’ Guide to

Eta Cassiopeiae

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    Also known as Achird, this binary consists of a Sol-like star with an orange companion, like Alpha Centauri without the Proxima component.

Location in Space

Radial Distance:

    Parallax = 0.16798±0.00048 arcseconds, which leads to;

        1. 19.42±0.06 lightyears (5.95±0.02 parsecs).

        2. 1,227,277±4125 AU.

Equatorial Coordinates:

    Right Ascension; 0 hr, 49 min, 06.2907 sec +7.244t sec.

    Declination; +57 deg, 48 min, 54.6758 sec -055.943t arc-sec.

        [elapsed time measured in centuries, Jan 2000 is t = 0]

    Imagine standing on the north side of a plane in which Earth’s equator lies with the north celestial pole directly overhead and look toward the First Point of Aries (now in Pisces just southeast of the Circlet). Then look eastward (to the left) by 12-1/4 degrees and then north (up) by almost 58 degrees.

Ecliptic Coordinates:

    Ecliptic Latitude; +47.01 deg + 39.5832t arc-sec.

    Ecliptic Longitude; 139.75 deg + 115.6268t arc-sec.

        [elapsed time measured in centuries, Jan 2000 is t = 0]

    Look toward the First Point of Aries (the point on the sky that the sun occupies on the first day of spring), shift your gaze eastward along the Ecliptic (the line that the sun traces through the Zodiac in the course of a year) by 139-3/4 degrees, and then shift your gaze northward by 47 degrees along a line perpendicular to the Ecliptic.

Galactic Coordinates:

    Galactic Latitude; -5.06 deg - 55.44t arc-sec.

    Galactic Longitude; 122.62 deg + 108.91t arc-sec.

        [elapsed time measured in centuries, Jan 2000 is t = 0]

    Look toward the radio source Sagittarius-A by casting your gaze across the Orion-Sagittarius Gap toward the Sagittarius-Carina Arm of the galaxy and at a point about six degrees south of the Ecliptic on the west (right) side of Sagittarius and two degrees south of X Sagitarii (the point of the arrow in the Archer’s bow). Then move your gaze in an easterly direction along the plane of the Milky Way by 122-2/3 degrees. Then tilt your gaze by 5 degrees in a southerly direction, more or less straight downward, at right angles to the plane of the Milky Way.

Annual Proper Motion

    in Right Ascension = 1.08659 arc-sec/yr = 6.17 AU/yr = 30.67 km/sec.

    in Declination = -0.55943 arc-sec/yr = 3.33 AU/yr = 15.79 km/sec.

        Total Proper Motion = 1.22215 arc-sec/yr = 7.277 AU/yr = 34.496 km/sec in a direction 117.24˚ counterclockwise from due celestial north, 71.10˚ counterclockwise from due Ecliptic north, and 116.98˚ counterclockwise from due Galactic north.

    in Radial Distance = +10.0±0.1 km/sec = 2.11 AU/yr.

        Total motion = 7.577 AU/yr = 35.92 km/sec.

    From the present; in 148,400 years Eta Cassiopeiae will become an eclipsing binary (for about 40 years) as its orbital plane passes over the Sol-Eta Cassiopeiae line and in 45,152 years ago Eta Cassiopeiae reached its perihelion 18.65 lightyears (1,179,290 AU) from Sol in the eastern part of the constellation of Draco, near the border with Cygnus, then crossed 43.84 degrees of sky to reach its present position.

Orientation in Space

    Orbit size: 71 AU = the semi-major axis of the combined orbits of the two stars in mutual revolution about their common barycenter. The ellipse of the orbit has eccentricity, e=0.497. The minimum (periastron) and maximum (apastron) separations between the two stars = 36 – 106 AU.

    We refer the following to the plane of the sky, which we define as the plane comprising all straight lines that cross our line of sight through the barycenter of the system under study and that pass through that barycenter. One of those lines coincides with the system’s line of nodes, the line where the system’s orbital plane crosses the plane of the sky. As a matter of definition, astronomers refer to the node where the system’s secondary crosses the plane of the sky moving at least partly away from Earth as the ascending node.

    Inclination; the angle between the plane of the stars’ orbits and the plane of the sky. Imagine laying the orbit flat on our line of sight to the target star system. In that orientation the stars would appear to us to move from side to side on a straight line. We define that inclination as 90˚ and we measure the actual inclination of the system by an angle between 0˚ and 180˚. If the system has an inclination less than 90˚, the stars appear to revolve counterclockwise about our line of sight (which we imagine always passing through the system’s barycenter) and we call the orbit prograde. If the system has an inclination greater than 90˚, the stars appear to revolve clockwise about our line of sight and we call the orbit retrograde.

i=34.76 degrees.

    Position angle of the secondary’s ascending node; the angle between the Equatorial north vector and the line of nodes, measured counterclockwise from the line pointing Equatorial north toward the system’s ascending node.

Ω=98.42 degrees.

    Longitude of Periastron (or Argument of Periastron); the angle between the line of nodes and the orbit’s major axis (line of apsides), measured from 0 to 360 in the prograde direction (the direction of the secondary’s motion) in the plane of the true orbit, from the secondary’s ascending node to the secondary’s periastron

ω=88.59 degrees.

    On a piece of stiff paper draw an ellipse of eccentricity equal to that of the orbit and draw an arrow indicating the direction of the star’s motion on the orbit that the ellipse represents. Imagine standing on the Equatorial plane with the Equatorial north pole directly overhead. Look toward the target star and so hold the paper that the line of apsides coincides with your line of sight and the north vector of the orbit (defined by the right-hand rule: when your right thumb, extended in a thumbs-up gesture, points north, the fingers of that hand curl in the same way that the body moves on its orbit) points Equatorial north. Designate the farther focus of the ellipse as the barycenter, the system’s center of mass. In that orientation your ellipse has a position angle of +270 degrees, an inclination of 90 degrees, and a longitude of periastron of 90 degrees. Rotate the paper counterclockwise about the line of apsides by 8.42 degrees (clockwise if you get a negative number). Turn the paper 181.41 degrees in the retrograde direction about the orbit’s north vector. And then tilt the paper 55.24 degrees about the line of nodes, turning the paper by the left-hand rule, the rule stating that when the thumb of your left hand points from the orbit’s ascending node to its descending node, the fingers curl in the direction you must turn the paper. With the paper in that position you have a picture of the orbit of the system’s secondary star. The ellipse represents the orbit of the system’s primary star if you change the position of the barycenter from one focus of the ellipse to the other.

    Orbital Period: 480 years.

        Time of Periastron passage: calculated out to AD 2300 from Twentieth Century. The presentation format is:

            1. 1889.6 (AD 1889 Jul 07)

            2. 2369.6

The Stars Themselves

    Star A:

        Diameter; 1,445,627±5289 km (1.0386±0.0038 Sol).

        Harvard Class; G0V (5,973±8 Kelvins).

        Age; 5.4±0.9 billion years.

        Mass; 0.972±0.012 Sol.

        Brightness; 1.2321±0.0074 Sol.

        Habitable zone: 1.26±0.06 AU, 490±50 days.

        Surface composition: hydrogen 74.375%, helium 24.725%, other 0.9% (Sol = hydrogen 73.7%, helium 24.5%, other 1.81%)

    Star B:

        Diameter; 918,654 km (0.66 Sol).

        Harvard Class; K7V (4,036±150 Kelvins).

        Age; 5.4±0.9 billion years

        Mass; 0.57±0.07 Sol.

        Brightness; 0.06 Sol.

        Habitable zone: 0.355±0.018 AU, 103±10 days.

        Surface composition: hydrogen 74.375%, helium 24.725%, other 0.9% (Sol = hydrogen 73.7%, helium 24.5%, other 1.81%).

Planetary system properties:

    stable planetary orbits lie within 1/5 of closest approach of components, 7.2 AU in this case.

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