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Modified Newton-Raphson methods for preliminary orbit determination

โœ Scribed by Edward T. Pitkin; Gilbert C. Carpenter

Publisher
Springer Netherlands
Year
1969
Tongue
English
Weight
968 KB
Volume
1
Category
Article
ISSN
1572-9478

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## Abstract In this paper, we propose the following modified Newtonโ€“Raphson iteration formulation: In case __r__=1, the obtained formulation reduces to the Newtonโ€“Raphson formulation. The present technique circumvent pitfalls of the Newtonโ€“Raphson iteration method. Some examples are illustrated.

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Starting with p = 37 as an approximation to its highest root a = 36 we get successively x 1 -36 = 0.184ร—10 0 , 0.759ร—10 -2 , 0.137ร—10 -4 , 0.445ร—10 -10 , 0.0 x 2 -36 = -0.141ร—10 0 , -0.732ร—10 -2 , -0.137ร—10 -4 , -0.445ร—10 -10 , 0.0 (x 1 + x 2 )/2-36 = 0.212ร—10 -1 , 0.135ร—10 -3 , 0.934ร—10 -8 , 0.0 (1