Appendix: \"Is Pluto a Planet ... \"

APPENDIX TO ABSTRACT: IS PLUTO A PLANET? YES ACCORDING TO A NEW MODEL FOR PLANET ORBIT PERIODS Theodore G. Mihran Schenectady NY July 27, 2015 The purpose of this Appendix is to supply the mathematical details between the equations given on the first page and the model factors given on the second page of this Abstract. On the second page the mathematical model is shown to consist of the product of three factors. The factors are given by the final three columns of the Table on p.2. From this Table for the outer planets the product of these three factors is: T(m)/T(J) = ½ * 2m * (2m+3)/2 = m2 + 3/2*m = m2 + m + m/2 = m*(m+1) + m/2

(1a)

(1b)

For the inner planets the product of the three factors is: T(J)/T(m) = ½ * (2|m|+1) * (2|m|+1)/2 = ¼ * (4m2 + 4|m| + 1) = m2 + |m| + ¼ = |m|*(|m|+1) + 1/4

(2a) (2b)

It is interesting that (1a) and (2a) in their three-factor form appear to be quite different, but they can be algebraically reduced to (1b) and (2b), which are quite similar. For any m the arithmetic can be done in your head. As an example, consider Earth for which m = -3. Since Earth is an inner planet, (2b) applies. Simply multiply 3*4 = 12 and add 0.25, giving 12.25. Neptune (m = 3) is the corresponding outer planet to Earth, so we again multiply 3*4 but add 3/2, giving 13.5. These values are the model values given in Column 3 of the Table on p. 2 of the Abstract. Similarly, for any m, multiply m by m+1 and add the appropriate term, m/2 for the outer planets and ¼ for the inner planets. It is significant that these equations correctly predict the measured ~10% difference between orbit periods of the outer planets and the reciprocals of orbit periods for the corresponding inner planets. This Appendix completes the Abstract of the paper “IS PLUTO A PLANET? YES, ACCORDING TO NEW MODEL FOR PLANET ORBITS”. The complete paper will be written in two parts. In Part 1 the origin of Table shown in the Abstract will be explained, but not physically justified in a rigorous manner. It is planned that In Part 2 the rigorous physical justification of the three factors of the model will be given.