Astronomy Dr. Denise Meeks [email protected] http://denisemeeks.com/science/notebooks/notebook_astronomy.pdf Astronomy: Earth Astronomy: Equinoxes and Solstices equinox: when the plane average standard of Earth's equator passes density atmosphere through the center of the mass (kg) radius (km) (gm/cm3) (pascals) Sun, occurs around Mar. 24 20 and Sep. 23 5.97 x 10 6,378 5.514 101,325 solstice: when the Sun mean distance reaches its most northern from Sun perihelion aphelion or southern excursion (km = 1 AU) (km) (km) axial tilt relative to the celestial 1.496 x 108 1.471 x 108 1.521 x 108 23.450 equator; occurs around average escape Jun. 21 and Dec. 21 gravity orbital speed velocity orbital (Image source: 2 https://cbsboston.files.wordp (m/s ) (km/s) (km/s) eccentricity ress.com/2015/09/sky.jpg) 9.81 29.78 11.186 0.0167 Astronomy: Celestial Sphere Astronomy: Ecliptic celestial spere: an imaginary sphere of arbitrarily large radius, concentric with Earth; all objects in the observer's sky can be thought of as projected upon the inside surface (Image of the celestial sphere source: https://ww w.quora.co m/What-is- (Image source: the- https://en.wikipedia.org/wiki/Celestial_sphere; image source: Lunar and Planetary ecliptic) Institute) Astronomy: Milankovitch Cycles (1) Astronomy: Milankovitch Cycles (2) Milankovitch cycles: describes the collective effects of changes in the Earth's movements on climate; theory that variations in eccentricity, axial tilt, and precession of Earth's orbit strongly influenced climatic patterns eccentricity: Earth's orbital eccentricity varies between nearly circular, with (Source of (1): the lowest eccentricity of 0.000055, and mildly elliptical, highest eccentricity https://en.wikipedia.org of 0.0679, with the mean eccentricity of 0.0019 /wiki/Milankovitch_cycl axial tilt: varies with respect to the plane of Earth’s orbit; slow 2.4° obliquity es) variations take approximately 41,000 years to shift between 22.1° and 24.5° and back again; when obliquity increases, amplitude of the seasonal cycle in (Image source: insolation increases, summers in both hemispheres receive more radiative https://en.wikipedia.org solar flux, and less in winters; when the obliquity decreases, summers receive /wiki/Milankovitch_cycl less and winters receive more es#/media/File:Precessi on_and_seasons.svg, precession: trend in direction of Earth's axis of rotation relative to fixed stars, Krishnavedala, CC BY-SA period of about 26,000 years; gyroscopic motion is due to tidal forces exerted 3.0) by the Sun and the Moon on Earth; both contribute equally to this effect. Astronomy: Sidereal and Synodic Periods (1) Astronomy: Sidereal and Synodic Periods (2) Earth Moon sidereal prograde motion: sidereal rotation sidereal orbital period in synodic period length of sidereal day length of solar day period in hours period in days days in days length of sidereal day 23h 56m 4.099s 365.25636 27.32166 29.53059 1 orbital period sidereal period: amount of time that it takes an object to make a full retrograde motion: orbit, relative to the stars; the sidereal day is 23h 56s length of sidereal day synodic period: amount of time that it takes for an object to reappear length of solar day length of sidereal day at the same point in relation to two or more other objects 1 1 1 1 orbital period synodic period between two bodies Psyn P1 P2 P1 and P2 are the orbital periods of the two bodies Astronomy: Sidereal and Synodic Periods (3) Astronomy: Equation of Time On a prograde planet like apparent solar time: time indicated by a sundial Earth, the stellar day is shorter mean solar time: average as than the solar day. At time 1, indicated by well-regulated the Sun and a certain distant clocks star are both overhead. At equation of time: difference time 2, the planet has rotated between apparent solar time 360° and the distant star is and mean solar time overhead again but the Sun is above the axis: sundial will not (1→2 = one stellar day). It appear fast relative to a is not until a little later, at time clock; below the axis sundial 3, that the Sun is overhead again (1→3 = one solar day). will appear slow (Image source: (Image source: https://en.wikipedia.org/wiki/Earth%27s_rotation#/media/File:Sidereal_day_(prograde) https://en.wikipedia.org/wiki/Equation_of_time#/media/File:Equation_of_time.svg, .png, Gdr, CC BY-SA 3.0) Drini, CC BY-SA 3.0) Astronomy: Universal Time and Coordinated Universal Time Astronomy: Julian Date and GMST 14 month universal time: time standard based on Earth's rotation; modern a floor y year 4800 a m month 12a 3 12 continuation of Greenwich Mean Time (GMT), the mean solar time on 153m 2 y the Prime Meridian at Greenwich, London, UK JDN day floor 365y floor 5 4 Coordinated Universal Time (UTC): primary time standard by which y y floor floor 32045 the world regulates clocks and time; is within about 1 second of mean 100 400 solar time at 0° longitude; does not observe daylight saving time hour12 minute second JD JDN (Sources: https://en.wikipedia.org/wiki/Universal_Time, 24 1440 86,400 https://en.wikipedia.org/wiki/Coordinated_Universal_Time) D JD-2451545.0 GMST 18.697374558 24.06570982441908*D Astronomy: Time Zones Astronomy: Kepler’s Laws 1. The orbit of a planet is an ellipse with the Sun at one of the two foci. 2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. P2 a3 (Image source: (Image source: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#/media/File:Kepl https://en.wikipedia.org/wiki/Time_zone#/media/File:Standard_World_Time_Zones.pn er_laws_diagram.svg, Hankwang, CC BY 2.5) g, TimeZonesBoy, CC BY-SA 4.0) Astronomy: Orbits (1) Astronomy: Orbits (2) GM 2GM retrograde motion: motion backward from the norm orbital speed v escape speed v perigee: point in the orbit of the moon or a satellite at which it is r r -11 2 2 nearest to Earth gravitational constant G = 6.67408 x 10 N m /kg apogee: point in the orbit of the moon or a satellite at which it is M = mass of body around which object is orbiting furthest from Earth r = distance of orbiting body from the center of mass M perihelion: point in the orbit of a planet, asteroid, or comet at which it GMm is closest to the sun gravitational potential energy U r aphelion: point in the orbit of a planet, asteroid, or comet at which it GM is furthest from the sun orbital period 2 3/ 2 gravity g periapsis: the point in the path of an orbiting body at which it is T r 2 GM r nearest to the body that it orbits 2 apoapsis: the point in the path of an orbiting body at which it is two massive bodies orbiting each other: T r 3 / 2 farthest from the body that it orbits G(M 1 M 2 ) Astronomy: Orbit Classifications (1) Astronomy: Orbit Classifications (2) altitude classifications eccentricity classifications low Earth orbit (LEO): orbits ranging in altitude from 160 circular orbit: has an eccentricity of 0 and path traces a circle kilometers (100 statute miles) to 2,000 kilometers above mean elliptic orbit: eccentricity greater than 0 and less than 1 whose orbit sea level traces the path of an ellipse Hohmann transfer orbit: orbital maneuver that moves a spacecraft from medium Earth orbit (MEO): orbits with altitudes at apogee one circular orbit to another using two engine impulses ranging between 2,000 kilometers and that of the geosynchronous transfer orbit: geocentric-elliptic orbit where perigee is geosynchronous orbit at 35,786 kilometers at the altitude of a low Earth orbit (LEO) and apogee at altitude of a geosynchronous orbit (GEO): circular orbit with an altitude of geosynchronous orbit 35,786 kilometers; period equals one sidereal day, coinciding with highly elliptical orbit (HEO):-geocentric orbit with apogee above 35,786 the rotation period of the Earth km and low perigee of about 1,000 km that result in long dwell times high Earth orbit (HEO): altitudes at apogee higher than that of the near apogee geosynchronous orbit (Source: https://en.wikipedia.org/wiki/Geocentric_orbit) Astronomy: Orbital Elements (1) Astronomy: Orbital Elements (2) eccentricity (e): shape of the ellipse, describing how much it is elongated compared to a circle ra rp semimajor axis (a): sum of the periapsis and apoapsis distances divided by e rp = perihelion distance ra = aphelion distance two ra rp inclination (i): vertical tilt of the ellipse with respect to the reference plane rp ra GM longitude of the ascending node (Ω): horizontally orients the ascending a object circular velocity vc node of the ellipse with respect to the reference frame's vernal point 2 a argument of periapsis (ω): defines the orientation of the ellipse in the 1 e 1 e orbital plane, as an angle measured from the ascending node to the perihelion velocity v p vc aphelion velocity va vc periapsis 1 e 1 e true anomaly (ν) at epoch(M0): defines the position of the orbiting body along the ellipse at a specific time (the "epoch") 2 1 velocity at distance r vr GM r a Astronomy: Celestial Coordinate Systems (1) fundamental plane coordinates primary direction coordinate system center point (0° latitude) poles latitude longitude (0° longitude) horizontal observer horizon zenith, altitude (a) or azimuth (A) north or south point (also called Alt-Az) nadir elevation of horizon equatorial center of the Earth celestial equator celestial poles declination (δ)