observation and reduction of occult at ion of stars by the moon, bohjelian

8/8/2019 Observation and Reduction of Occult at Ion of Stars by the Moon, Bohjelian

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AUG 17 i

Observation and Reduction of Occultations ofStars by the Moon

WITH A DETERMINATION OF THE RESULTING LONGITUDE OFTHE FLOWER OBSERVATORY, AND CORRECTIONS TO THERIGHT ASCENSION, DECLINATION AND SEMI-DIAMETER

OF THE MOON

BYKRIKORIS GARABED BOHJELIAN

A THESISPRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE

UNIVERSITY OF PENNSYLVANIA IN PARTIAL FULFILMENTOF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

UN!\

PRESS OFTHE NEW ERA PRINTING COMPANYLANCASTER, PA.1915


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Observation and Reduction of Occupations ofStars by the Moon

WITH A DETERMINATION OF THE RESULTING LONGITUDE OFTHE FLOWER OBSERVATORY, AND CORRECTIONS TO THERIGHT ASCENSION, DECLINATION AND SEMI-DIAMETER

OF THE MOON

BYKRIKORIS GARABED BOHJELIAN

A THESISPRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE

UNIVERSITY OF PENNSYLVANIA IN PARTIAL FULFILMENTOF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

PRESS OFTHE NEW ERA PRINTING COMPANYLANCASTER, PA.

1915


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INTRODUCTION.It is well known that corrections to the coordinates, distance,

and size of the Moon can be determined from the observationsof occultations more accurately than from any other method.

If simultaneous observations of this kind are secured from twostations on the Earth, which differ widely in latitude, the oblate-ness of the Earth can also be found ; and whatever the situationof the stations, their difference in longitude can be thus deter-mined with a higher accuracy than by any other method, exceptthat of the Telegraph and Wireless.As the Longitude of the Flower Observatory was accuratelydetermined, both by Telegraph and Wireless method, a com-parison of these results with a value found from occultationsbecomes of interest, and as the later observations have a specialvalue for improving our knowledge of the Moon's motion, thefollowing piece of work was undertaken with these objects.The work was begun in the early summer of 1914, the obser-vations being made with the 1 8-inch equatorial of the FlowerObservatory of the University of Pennsylvania.Among the occultations observed it. was learned that 13 hadbeen simultaneously observed by Prof. Asaph Hall, with the26-inch equatorial of the U. S. Naval Observatory.Through the courtesy of the Director, Captain J. A. Hooge-

werff, these observations were forwarded to Prof. Eric Doolittle.It is the results from these stars, which form the principal

basis of the following investigation.OBSERVED TIMES OF OCCULTATIONS.

Date, 1914


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OBSERVATION AND REDUCTION OFPRELIMINARY COMPUTATION.

The right ascension and declination of the above stars, reducedto apparent place for the observed times are as follows:

Date, 1914


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OCCULTATIONS OF STARS BY THE MOONDate


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6 OBSERVATION AND REDUCTION OFwhere for Phila.


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OCCULTATIONS OF STARS BY THE MOONand ^ we next compute 12, T, x, v, from the formulae:

12 = h [-cos 4, - -cos (M - N) 1 - (/' - t) h = 3600In n Jf-p __ J. J^n sin N yo cos

#o cos N yo sin N


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8 OBSERVATION AND REDUCTION OFFORMATION OF THE FINAL EQUATIONS OFCONDITIONS.

Writing the results thus far obtained, we may now set up thefollowing equations, which we divide into four groups :

W = 5hW =W =W =W =W =W = 5W =W =W =W = 5

July 17.


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OCCULTATIONS OF STARS BY THE MOON 9It is evident, however, that for various reasons a direct

solution of these equations in each group will not be expedient.In the first place, the large terms involved would render theoperation very laborious, and furthermore, it will not be possibleto separate ATT from the remaining quantities, without assumingboth w and wr to be known.We therefore proceed as follows: Assuming the equations ofequal weight, we subtract the first from the third, the third fromthe fifth, etc.; and the fourth from the second, the sixth from thefourth, etc.; continuing thus we obtain the following groups ofequations :

Group I' 24-


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IO OBSERVATION AND REDUCTION OFknown a priori that such was the case, it would be shown fromthe normal equations, which would be practically indeterminatefor this quantity.We should, therefore, determine & and nAk in terms of ATT,in order to see what effect an error in TT will have upon thelongitude.We derive from the above equations, for groups I '2 and 1 1 '2,only, the following two sets of normal equations; the last twogroups are solved as they stand, since there are two equationsin each group. Normal to Group I' 2 (or I' 3)+ II.Slz? 2I.237TA/C = + 10.07ATT + I4-5O

21.231? + i33.057rA/c = 62.5IA7T 14.89Normal to Group IT 2 (or 11' 3)+ 6.54$ 12.47^ = + 7.27A?r + 51.9

12.40?? + I28.6TA/C = 48.3OA7T 186.6From I '3 we obtain

& = + 1.428 + .ooSATT?rA& = + o.i 12 470A7T

To find 7 we now substitute these values in (i), (3), (5), (7),and (9), and observing that wf 5h 8m i5 s-78, we find the meanvalue of 7 to be

7 = + 6".52 - .639A7TWe now substitute these values of #, 7rA&, 7 in (2), (4), (6),(8), (10), (30), (40), when we find the following values for the

difference of longitude between Greenwich and the FlowerAstronomical Observatory of the University of Pennsylvania:

W = 5*1 jm 78^7 _j_ .07A7Tw = 5 i 6 .99 .40w = 5 i 6 .49 - .07w = 5 i 6. 53 + .39w = 5 i 6 .51 + .29w = 5 i 6 .89 .48= 5 i 7 -54 ~ -27

Mean w = 5h im 6S.96 .o6A7r


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OCCULTATIONS OF STARS BY THE MOON IIAnd the resulting longitude from Washington is

\ = 7m 8S.82 - .06A7TWith the above values of y and & we may now determine correc-tions to the assumed right ascension and declination of the Moon.We have the formulae :

sin N cos D Aa + cos N. A5 = 7cos N cos D Aa sin N. A5 = #

and from theseAa = + 6".58 A5 = +- 2".Q6

Assuming the errors of the star places to be inappreciable, thesewill represent the errors in the computed right ascension anddeclination of the Moon at a time corresponding to the mean oftimes of the observations.These corrections, it will be seen, are affected by any small

outstanding error in the parallax, as they have been derived byassuming ATT = o.In the same way, assuming Ax = o and taking the mean of thevalues given above, viz: 329 1" we find from the above value of

-f- ."ii 2 A& = -f- .000034we have assumedtherefore,

k = + .272506k = + .272540

as shown from these observations.In the same way by solving the other groups of equations, we

obtain the following results:Group


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12 OBSERVATION AND REDUCTION OF OCCULTATIONS OF STARSCONCLUSION.

The errors Aa and A5 in the Moon's position are somewhatsmaller than was to be expected, and indicate that this body isfollowing its computed path somewhat more closely than inrecent years.The corrections A& to the apparent semi-diameter is markedlynegative, but it is possible that values of this quantity securedfrom occultations may be influenced by the aperture of theinstrument employed.The final mean value of longitude of Flower Observatory fromU. S. Naval Observatory, as shown above, from this work is

X = 7* 88.87The results previously obtained for the same quantity are:

By Telegraph X = - ym 8s.9iBy Wireless X = - 7m 8*74

observation and reduction of occult at ion of stars by the moon, bohjelian

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