Comenius project « In orbit with Europa »

Parallax André Debackère Collège “Le Monteil” Monistrol sur Loire FRANCE June 2013

To lead this project we chose to use the Faulkes telescope because they have the advantage of being located in the night during the day in Europe (11h UT in Europe, 21h LT in Siding Spring and 1h LT in Hawaii). UT : Universal Time and LT : Local Time

Other advantage: the two sites have identical instrumentation; twin telescopes (2 meter telescope class) and the same CCD camera (Fairchild CCD486 BI).

I) Measuring the parallax shift We took 2 images of the asteroid (270) Anahita on March 29th 2013 simultaneously from FTN and FTS. Slots UT RA 11H30/11h59 11h20m05.1s

Dec +00°12’09’’

FTN 11h45m17s The Leigh Technology Academy Dartford UK

name (270) Anahita

FTN Conrad’ team UK

FTS Andre’ team FR

FTS 11h45m18s College Le monteil Monistrol sur Loire FR

1) Using ALADIN to calibrated the field of view of the two telescopes

Coordinates of 2 reference stars: NOMAD Catalog S1: 0902-0204254 11h20m13.311s +00°12’05.79’’ S2: 0901-0205704 11h19m48.876s +00°11’56.00’’ 1) Using SalsaJ Coordinates of the 2 reference stars measured on our 2 images: FTN image S1: 11h20m15.63s +00°11'46.31'' S2: 11h19m50.96s +00°11'36.58'' FTS image S1: 11h20m13.32s +00°12'05.31'' S2: 11h19m48.88s +00°11'56.20'' The coordinates of these two stars measured with SalsaJ differ significantly for the image obtained by FTN and a very little for the image obtained by FTS.

2) Measure of the asteroid shift on the 2 images in respect to one reference star. a) Calculation of the distance between the 2 stars S1 et S2 in arc-seconds from their coordinates: ΔRA = 11h20m13.311s - 11h19m48.876s et ΔDec = +00°12’05.79’’ - +00°11’56.00’’ ΔRA = 24.435s et ΔDec = 9.79’’

Conversion of ΔRA in arc-seconds ΔRA(’’) = ΔRA(s) x 15.041084° x cos 0.2° (360° →23h56m04s and Dec = 12’ = 0.2°) ΔRA(’’) = 24.435 x 15.041084 x 0.9999939 ΔRA(’’) = 367.53’’ d2(‘’) = ΔRA2(’’) + ΔDec2(‘’) d(‘’) = 367.66’’ b) Measure of the distance in pixels between these 2 stars on each image : Using SalsaJ

FTN image: S1S2= 1224.54 pixels FTS image: S1S2= 1209.31 pixels c) Calculation of the pixel value on each image: FTN image: 367.66’’/1224.54 pix soit E1 = 0.3002433’’/pix FTS image: 367.66’’/1209.31 pix soit E2 = 0.3040246’’/pix d) Shiftings: Measures of East-West and North-South shifts Δ X and Δ Y of the asteroid with SalsaJ on: FTN and FTS images with reference star S1 FTN and FTS images with reference star S2 e) ρ2= Δ X2 + Δ Y2 We do that for the 2 reference stars Average of our measures ρ (‘’) = 6.914 +/-0.304

II) Calculation of the baseline B 1)

Distance FTN-FTS =B 3) To determine the parallax of an object in our Solar system, we must know the length of the baseline used to make observations. Geographic coordinates of the Faulkes telescope : -

LCOGT data a) FTN 20° 42’ 27’’ N or ϕA=20.71° N 156° 15’ 21.6’’ W or λA=156.26° W H = 3055 m b) FTS 31° 16’ 23.88’’ S or ϕB=31.27° S 149°04’ 15.6’’ E or λB=149.07° E H = 1116 m

dλ=λB-λA dλ=54.75° β=sinϕA sinϕB + cosϕA cosϕB cosdλ β= 73,88258°

AM=sinβ x RT RT = 6378 km AM = 3833.15 km Baseline FTN/FTS B=AM x 2 B=7666.30 km ρ/2 = 6.914 (’’)/2 = 9.602777 10-4 (°) D=( B/2) /( tanρ/2) D=228708130.2km (distance between the asteroid and the baseline) Or the declination of the asteroid Anahita was +00°12’ and the latitude of point M’ (projection of M on the surface of the Earth) is -5.3°, we can say that O, M and M’ are nearly aligned. Calculation of MM’ MM’ = OM’-OM MM’ =RT-RT x cos (β/2)

MM’ = 1280.37 km Compared with M’ on the surface of the Earth located between FTN and FTS, the asteroid Anahita is supposed to be at about 228706850 km The website JPL Horizon give us about 228368035 km (interpolation between 11h45m00s et 11h46m00s). Final error :0.15%

Thanks to Frédéric Merlin, Paris-Meudon Observatory, who helps us to do these calculations.