ECCENTRIC ANOMALY. ey 



N°. VIII. 



A letter from Mr. Andrew Ellicott, to Mr. Ro- 

 bert Patterson. 



A Method of Calculating the Eccentric Anomaly of the Planets. 



Philadelphia, April 4th, 1 794. 



Sir, 



Read April T TAVING occafioii foiTie years ago to conftruifl: a fet 

 4, 1794. JlI of agronomical tables for the planet ft, I made 

 ufe of an operation to obtain the eccentric anomaly, the firfl 

 part of which I believe to be new ; the fecond, is fimilar to the 

 method made ufe of by Sir Ifaac Newton in his Principia. — He 

 firil affumcs an arc, and then proceeds to find its error : but by 

 the method which I have purfued, we proceed directly to the 

 folution of the problem M'ithout any affumption, and therefore 



adhere more clofely to the principles of geometry. The firfl 



part of the operation will give the eccentric anomaly almoft fuf- 

 ficiently exail: for any of the planets belonging to our fyftem ; 

 and the fecond which is very eufy, will produce a greater 

 degree of exaftnefs than is requifite for any of the bodies revol- 

 ving round our Sun, the comets excepted. The method is as 

 follows. 



Let S, Fig. g. Plate L reprefent the Sun, and the arc AN the 

 mean anom.aly ; join, SN — through the centre C ; draw CP 

 parallel to SN, and the angle ACP will be nearly the eccentric 

 anomaly ; and may be had by the following analogy. — From 

 the log. tang', of half the mean anomaly, fubtraft the difference 

 of the logs, of the aphelion and perihelion diftances, the remain- 

 der will be the log. tang', of an angle, to which add half the 



mean anomaly, and the fum will be the angle ACP. For 



an example, take the planet ft. 



Let the mean ani^malyAN^6o''thehalf 30° log. tapg^ — 9.76i43<)4 



T D -i^r 1-ci £' '''I- Dedufl the difference — 0.0413640, and 

 Log.Ftrihelion dift. 6.25940523 2_iJr:'" 



there remains log. tang'. 9.7200754 which 



anfwers 



