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Coordinate Systems: Alt, El, Az, Zenith Angle

Zenith Angle. Elevation or Altitude. Coordinate Systems: Alt, El, Az, Zenith Angle. Coordinate Systems: Alt, El, Az, Zenith Angle. Azimuth. Celestial Sphere. Coordinates on Celestial Sphere. One hemisphere… view from inside.

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Coordinate Systems: Alt, El, Az, Zenith Angle

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  1. Zenith Angle Elevation or Altitude Coordinate Systems: Alt, El, Az, Zenith Angle

  2. Coordinate Systems: Alt, El, Az, Zenith Angle Azimuth

  3. Celestial Sphere

  4. Coordinates on Celestial Sphere

  5. One hemisphere… view from inside

  6. Map from inside of Cel. Sphere, looking out

  7. Map from inside of Celestial Sphere of radio sky

  8. Zero of R.A. coordinate system tied to intersection of Ecliptic Plane with Equatorial Plane The Vernal Equinox

  9. Moon’s orbit inclined ~5 deg w.r.t. plane of ecliptic:

  10. after ~4.65 (=18.6/4) years, ….

  11. after ~9.3 years,…

  12. after 18.6 years… Moon orbit has regressed full turn…

  13. 6 hours Local Siderial Time = LST observer’s location 12 hours 18 hours Vernal Equinox RA=0 N.P.

  14. Dec RA

  15. 6 hours LST observer’s location 12 hours 18 hours HA = Hour Angle HA RA Vernal Equinox N.P.

  16. 6 hours HA = Hour Angle LST HA observer’s location 12 hours HA = LST - RA LST = HA 18 hours RA Vernal Equinox N.P.

  17. 6 hours LST 12 hours 18 hours Sun Vernal Equinox RA=0 N.P. Solar Time = hours since midnight

  18. 6 hours GST 12 hours 18 hours Sun Greenwich Vernal Equinox RA=0 N.P. Greenwich Time …. becomes UTC = Coordinated Universal Time

  19. 6 hours observer’s location Local Siderial Time = LST Vernal Equinox RA=0 12 hours N.P. 18 hours

  20. One hemisphere: future North Poles

  21. Zero of R.A. coordinate system tied to intersection of Ecliptic Plane with Equatorial Plane The Vernal Equinox

  22. motion of RA=0, Decl=0 (J2000) in past and future Epochs… Current epoch called `epoch of date’ (at equator, 4 minutes of time = 1 degrees)

  23. Spherical Trigonometry & Spherical triangles sides are portions of great circles

  24. PCD is a spherical triangle PAB is NOT a spherical triangle

  25. c A

  26. Spherical triangles sin Asin Bsin C sin a sin b sin c = = cos c = cos a cos b + sin a sin b cos C

  27. Radio Astronomy Overview Radio `source’ • Goals of telescope: • maximize collection of energy (sensitivity or gain) • isolate source emission from other sources… (directional gain… dynamic range) Collecting area

  28. LOFAR “elements”

  29. thought experiment… 2 wires out (antennas are “reciprocal” devices… can receive or broadcast)

  30. thought experiment… Black Body oven at temperature = T

  31. Black Body oven at temperature = T thought experiment… R

  32. Black Body oven at temperature = T thought experiment… … wait a while… reach equilibrium… at T R warm resistor delivers power P = kT B (B = frequency bandwidth; k = Boltzmann Const)

  33. R real definition… Measure Antenna output Power as “Ta” = antenna temperature Ta temp = T warm resistor produces P = kT B = Pa = kTa B

  34. Q Radio `source’ Reception Pattern or Power Pattern Collecting area

  35. Radio `source’ If source with brightness temperature Tb fills the beam (reception pattern), then Ta = Tb Collecting area (!! No dependence on telescope if emission fills beam !!)

  36. receiver “temperature”… quantify Receiver internal noise Power as “Tr” = “receiver temperature” Ta Ampl, etc Real electronics adds noise …treat as ideal, noise-free amp with added power from warm R Tr+Ta Ampl, etc

  37. “system temperature”… quantify total receiver System noise power as “Tsys” Tsys+Ta Ampl, etc RMS fluctuations = DT DT = (fac)Tsys/(B tint)1/2 Fac ~ 1 – 2 B = Bandwidth, Hz tint = integration time, seconds

  38. Radio `point source’ Power collected = SnAeff B/2 Sn = flux density (watts/sq-m/Hz) [ 1 Jansky = 1 Jy = 10-26 w/sq-m/Hz ] Aeff = effective area (sq-m) B = frequency bandwith (Hz) Ta = SnAeff /2k Collecting area

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