A N O 



ANOMALISTIC Year. See Earth. Elements of, 

 ANOMALY, in Astronomy. (Maddy, Play fair.) 

 Given the mean anomaly (), to find the true (), (usually called Kep- 

 ler's Problem.) 

 1st Method. .If the eccentricity (<?} be rr/v/ small, 



1 4- e 

 tan. r ^ . tan. | w. 



2rf Method. Let M be the eccentric anomaly, and let the true and mean 

 anomalies be measured from aphelion ; then we have the following equa- 

 tions : 



M = u -\-e sin. if. 



/T^7 

 & tan. % r, V } . tan. u. 



Therefore, eliminating u between these two equations, the relation 

 between m and v may be found. 

 If the anomalies are measured from perihelion, 

 m u e sin. it. 



& tan. | v V y^ tan. I u. 

 The following is the series for v in terms of M. 



8in. 2 m + ( -~ <* - -gj- 5 ) sin. 3 m + (^ -^ <* - -^ e) sin 4 

 1(K)7 1223 



A'y^'. The constant coefficients must be reduced into degrees afnd 

 minutes, by multiplying each of them by 57. 29578, the number of de- 

 grees in an arc equal to the radius. 



'Ml Method. To find the true anomaly in terms of the mean, in a series 

 ascending by powers of /'. 



v m -j- 2 sin ?. e -f- -- sin. 2 m. e* -}- &c. 

 And to find m in terms of r, 



/// r (2 c 4 e. 1 c2) sin. v -f- (e 2 4 r <". 1 <T' sin. ^ r ^ 



\vliere <. ~ 



^! 



