* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download COMETARY PARALLAX
Survey
Document related concepts
Hubble Deep Field wikipedia , lookup
Impact event wikipedia , lookup
Theoretical astronomy wikipedia , lookup
Reflecting instrument wikipedia , lookup
Astrophotography wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Observational astronomy wikipedia , lookup
Geocentric model wikipedia , lookup
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Astronomical naming conventions wikipedia , lookup
Comet Hale–Bopp wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
Transcript
COMETARY PARALLAX StarFest 2005 Bays Mountain Preserve October 22, 2005 John C. Mannone Abstract Planetarium software and PowerPoint slide utilities are engaged to graphically determine the parallax of a near object observed by amateur astronomers. This graphical method seems to favorably compare with spherical trigonometry methods (not discussed). Though applicable to some planets and our Moon, the technique will be demonstrated with comets on close approach (~1 au). This is useful for planned coordinated viewing/photography and for a classroom experiment to determine distance of approach. The technique can be extended to very close objects such as satellites and meteors, but video imaging and processing will be required. Definition of Parallax What is it? When an object is viewed from two different positions, there is a shift in the apparent position of the object against a distant background. Shift can be caused by several things, e.g., Change in refractive index which bends the light Change in geometry (trigonometric parallax) (Spectroscopic parallax applies to determination of distance from spectroscopically determined luminosity and spectral class) Trigonometric Parallax A simple example: Look at me with one eye shut Then the other Note my apparent position against the backdrop is different Trigonometric Parallax Eyes are separated some base distance, b The angular difference of my image perceived by each eye (each viewing position) is the parallax (angle) related to the base distance and the my distance to the observer. The further away, the smaller the angle: Tycho Brahe tried to apply parallax in 1570’s, but Friedrich Bessel first successfully applied this to stars in 1838: 61 Cygni: 0.333” (modern result 0.289”). The closest star, Proxima Centauri, has largest p = 0.772” Stellar Parallax Stellar Parallax Stellar Parallax Stellar Parallax parallax angle distance Parallax, p, and distance, d, are related through simple geometry, especially when the the parallax is small, as it is in the case of stars. d (parsec) = 1/p (arcsec) 1 pc = 3.26 ly Cometary Parallax Comets approach much closer than stars, so expect parallax angle be much larger. Because of its rapid motion (relative to stars), a simultaneous observation will limit observation to different places on the Earth (instead of two different orbital positions of the Earth). This limits the distance between observation sites to the chord through the Earth connecting the two locations. A further reduction in the chord because of the comet’s perspective. The parallax will be larger only by an order of magnitude over nearby stars. Determination of Comet Approach Distance by Parallax Distance-Parallax Related through the Projected Chord tan (p/2) = b/2d d1 = d - R + (R2-b2/4)1/2 ~d for more distant objects p is the parallax (angle), b is the projected chord distance A”B” between the 2 observing sites A and B (perpendicular to the zenith line d1 at a point on the surface of the Earth directly beneath the comet at C). Comet’s apparent positions A” among background stars b R B” d1 d p C Determination of Cometary Parallax Graphical Software Simulation Photographic Analysis Image Overlap/Scaling Analytical Three-Dimensional Exact Solution- Celestial Sphere Spherical Trigonometry Why the Interest in Cometary Parallax? I purchased a personally autographed photograph of HaleBopp from Dr. Tom Bopp at UTC in March 2003. It is one of his favorite photographs by Bill and Sue Fletcher. I became interested in everything about the photograph: the photographic details, identification of the major stars. I reasoned others might have simultaneously photographed the comet, especially near closest Earth approach and wondered if the comet’s distance could be easily determined by comparing photographs. Synchronizing time is easy with planetarium software. Hale-Bopp Trajectory Near Perihelion Earth Closest Approach: March 22, 1997 (1.315 AU) Sun Closest Approach: April 1, 1997 03:14 UT (0.914 AU) “This is the beautiful Comet Hale-Bopp as it approached Earth in March of 1997. The solid portion or nucleus of the comet is made up of ice, frozen gases, dust and small rock. Compared to most comets Hale-Bopp is very large - about 35 kilometers in diameter. As its orbit brought it closer to the sun, the frozen mass began to melt and a coma, which is a gaseous cloud, developed around the nucleus. This coma has grown to be hundreds of thousands of miles in diameter. Finally the tail developed which became millions of miles long. This color photo reveals both the reddish cream-colored dust tail, and the many long blue streamers of the ion (gas) tail.” (photographers Bill & Sue Fletcher) TIME Picture of Year 1997, TIME/LIFE Picture of the Century 2000 Joshua Tree National Park "God just gave me a gift. I get to see things in the sky that the average person doesn't see…I think that what's out there is God's creation meant for our enjoyment." Wally Pacholka Date and Time: Camera: Film/Exposure: Length/Width Ratio: April 4, 1997, 8 PM PST 50mm Minolta lens f/1.7 on a tripod; Fuji 800 film (35 mm)/ 30 seconds 1.36 => picture cropped Joshua Tree located with the help of digital desert and aviation charts: Coordinates 34N, 116W Elevation 3000 to 4000 ft f = 50 mm, f/ = 1.7, D = 29.4 mm Approximate FOV: 2arctan [(36 x 24 mm/2)/50 mm] FOV = 27.0o x 39.6o Calculated FOV 1.15o x 1.72o “Comet Hale-Bopp photographed on the morning of March 8, 1997, from Stedman, N.C. This 10-minute exposure was made with a 12.5inch reflecting telescope (f = 1200 mm) and exposed on Fujicolor SG800 Plus film. The telescope tracked the comet during the exposure, rendering the stars as short lines. Hale-Bopp is moving northward against the stars at the rate of 1.5 degrees per day*. The comet continues to be visible to the naked eye in the predawn northeastern sky.” (Jim Horne, photo 33) ~50,000 mph HALE-BOPP March 8, 1997 9-hour time difference means photos taken at different local times Cathedral City, CA, USA Asagio, Vincenza, Italy HALE-BOPP March 8, 1997 (actually March 7) This Fletcher photograph was made with the special Schmidt camera/telescope. An 8-inch Celestron equivalent to a super fast (f/1.5) 305 mm telephoto lens. Equipped with curved film holder => no distortion along width. Joshua Tree National Park, CA, USA Wide field of view 4.5o x 6.75o HALE-BOPP March 7, 1997 4:40 AM This Fletcher photograph was made with the special Schmidt camera/telescope. Wide field of view 4.5o x 6.75o An 8-inch Celestron equivalent to a super fast (f/1.5) 305 mm telephoto lens. Equipped with curved film holder => no distortion along width Parallax by Graphical Methods Software Simulation Photographic Analysis Parallax is determined by superposition of images with the same field of view or scale. Both views are aligned. The transparency can be adjusted with the picture editing feature. This facilitates the correct overlapping. Angular separation between the comet and the star is determined (a standard feature on Starry Night Backyard software). The parallax is determined by comparison with the scaled cometstar distance. Hale-Bopp 100 degree field of view from Joshua Tree, California Hale-Bopp 30 degree field of view from Joshua Tree, California Hale-Bopp 15 degree field of view from Joshua Tree, California Hale-Bopp 1 degree field of view from Joshua Tree, California Hale-Bopp 1 degree field of view from Asagio, Italy USA Italian Italian USA Hale-Bopp 1 degree field of view overlays 68% transparency of top slide USA Italian Italian USA Hale-Bopp 1 degree field of view overlays Overlap Background Stars Hale-Bopp 1 degree field of view overlays Rotate to align along RA/Dec lines Italian Hale-Bopp 1 degree field of view overlays Re-establish Overlap Measure length; use ratio and proportion to obtain parallax Italian Measure angular separation on Starry Night; relate to scale length Hale-Bopp 1 degree field of view overlays Re-establish Overlap Using a different star, the results are summarized below Comet Hale-Bopp March 8, 1997 11:40Z Asiago, Italy 0.30 inch parallax Joshua Tree National Park, CA Parallax, p = (.30 inch) (249”/10-7/8 inch) = 6.87’’ +/- 10% Parallax by Analytical Methods Apparent Comet Positions Projected on Celestial Sphere A” CB R b C d1 p B” Projected Geographic Positions Celestial Sphere C CA Actual position of comet: C C p CA DDec CB DRA Apparent positions of comet from projected A and B Parallax seen on a Spherical Triangle The 3-dimensional Exact Calculation of Parallax Spherical Geometry A b c C B a Symbols in this graphic have different meanings Parallax is calculated from object’s equatorial coordinates from both locations using the law of cosines for spherical triangles cos c = cos a cos b + sin a sin b cos C = sin a' sin b' +cos a' cos b' cos C c parallax, a and b equatorial colatitudes, C equatorial longitude difference, a' and b' are the corresponding latitudes = 90-a and 90-b (degrees) Parallax by Analytical Methods Three-Dimensional Exact Solution- Celestial Sphere Spherical Trigonometry cos p = sin latA sin latB + cos latA cos latB cos (lonB-lonA) Need chord length to calculate distance and an understanding of the celestial rotating coordinate system Equatorial and Horizon Coordinates Courtesy of Scott Robert Ladd, “Stellar Cartography” Greenwich Mean Sidereal Time Hale-Bopp March 8, 1997 11:40Z Calculator by AstroJava “Sidereal time is the measure of the earth's rotation with respect to distant celestial objects. By convention, the reference points for Greenwich Sidereal Time are the Greenwich Meridian and the vernal equinox (the intersection of the planes of the earth's equator and the earth's orbit, the ecliptic). The Greenwich sidereal day begins when the vernal equinox is on the Greenwich Meridian. Greenwich Mean Sidereal Time (GMST) is the hour angle of the average position of the vernal equinox, neglecting short term motions of the equinox due to nutation.” Rick Fisher NRAO Green Bank, WV Projected Chord Determination Vector Analysis or Coordinate Rotation Using Transformation Matrices or Graphically using a Celestial Sphere model and string Not reviewed here Coordinate Information for Comet Hale-Bopp March 8, 1997 11:40Z Simultaneously Viewed from USA and Italy Hale-Bopp March 8, 1997 11:40Z Asiago Joshua Tree Joshua Tree Comet Coordinates J (now) Epoch from Starry Night Backyard v 3.1 RA 22h 15.348m = a Dec 39o 49.504’ = d GST = 22h 44m 51.7s Lat comet = d = 39.825067o Lon comet = H = a - GST = -29.514m @15o/hour H = -7.378417o Hale-Bopp March 8, 1997 11:40Z Asiago Joshua Tree Observer Coordinates (estimated) A- Joshua Tree LatA 33o 44.4’ N LonA 116o 25.2’ W Time Zone -7 hr => 4:40 am March 8, 1997 local daylight time B- Asiago LatB 48o 22.809’ N LonB 9o 37.331’ E Time Zone +1 hr => 12:40 am March 9, 1997 local standard time Lat comet = d = 39.825067o Lon comet = H = -7.378417o (from Joshua) Hale-Bopp March 8, 1997 11:40Z Asiago Joshua Tree Actual distance to Earth 1.382 AU From orbital parameters in Starry Night b = 6672.88 km from spherical trigonometry (compare to Earth radius of 6378 km) p = 6.87” from graphical method d1 =1.372 AU (0.72% high) Accurate, but imprecise (10%) p = 6.8319” from spherical trigonometry d1 = 1.385 AU (0.19% high) Accurate and precise d1 = (b/2)cotan(p/2) Conclusion 1) Graphical determination of parallax is effective with planetarium software, such as Starry Night, and PowerPoint picture options. Scanned photographs of simultaneous photographs would be analyzed in the same way. 2) Results are very accurate, though more difficult to reproduce than with spherical trigonometry. This was applied to Comet Hyakutake with superior results. 3) Procedure is sufficiently simple for secondary educational outreach and amateur astronomy, yet easily extended to collegiate level. 4) Extension to Lunar parallax using solar system objects like Jupiter as background is very effective. Conclusion 5) Extension to ISS is possible with the help of Heaven-Above website for satellite position and altitude. Video imaging and processing would be required to synchronize simultaneous observations. This would be a good calibration technique since the distance to the satellite would be known. 6) Extension to Meteoritic parallax is an advanced experiment similar to satellite tracking except for the uncertainty of when a rapidly moving meteor will appear. It’s height is unknown, but is in the ionosphere and could be determined.