Mathematical tracts on the lunar and planetary theories [&c.]. |
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Page 10
... PROP . 4. To find ( 0 - B ) in terms of nt + e - B , or the true anomaly in terms of the mean . - To a limited number of terms , this may be done by inde- terminate coefficients . Put y for 0 - B , z for nt + € −B ; assume y = z + a ...
... PROP . 4. To find ( 0 - B ) in terms of nt + e - B , or the true anomaly in terms of the mean . - To a limited number of terms , this may be done by inde- terminate coefficients . Put y for 0 - B , z for nt + € −B ; assume y = z + a ...
Page 12
... PROP . 5. The center of gravity of the Earth and Moon describes about the Sun , very nearly , an ellipse in one plane , and the area passed over by its radius vector is very nearly pro- portional to the time . Let E and M , ( fig . 1 ) ...
... PROP . 5. The center of gravity of the Earth and Moon describes about the Sun , very nearly , an ellipse in one plane , and the area passed over by its radius vector is very nearly pro- portional to the time . Let E and M , ( fig . 1 ) ...
Page 17
... PROP . 7. To find the resolved part of the disturbing force , which is parallel to the plane of the ecliptic , and perpen- dicular to the projection of the radius vector . The only force which acts in this direction on M is the re- m ...
... PROP . 7. To find the resolved part of the disturbing force , which is parallel to the plane of the ecliptic , and perpen- dicular to the projection of the radius vector . The only force which acts in this direction on M is the re- m ...
Page 19
... PROP . 10. To find the differential equations for the motion of M about the fixed center E. Let Ev , Fig . 3 , be a straight line in the plane of the ecliptic , drawn from E towards the first point of Aries : Mb perpendicular to the ...
... PROP . 10. To find the differential equations for the motion of M about the fixed center E. Let Ev , Fig . 3 , be a straight line in the plane of the ecliptic , drawn from E towards the first point of Aries : Mb perpendicular to the ...
Page 20
... obtain equations between p , 0 , and s , independent of t . This is the object of the next proposition . 32. PROP . 11. To eliminate t from the differential equa- tions . Since , in their present form , t is the 20 LUNAR THEORY .
... obtain equations between p , 0 , and s , independent of t . This is the object of the next proposition . 32. PROP . 11. To eliminate t from the differential equa- tions . Since , in their present form , t is the 20 LUNAR THEORY .
Other editions - View all
Mathematical Tracts on the Lunar and Planetary Theories George Biddell Airy No preview available - 2019 |
Mathematical Tracts on the Lunar and Planetary Theories George Biddell Airy No preview available - 2019 |
Common terms and phrases
2π λ analyzing plate angle angular velocity attraction axis bright Cambridge cloth co-ordinates coefficient Consequently constant cos² Crown 8vo crystal curve depending different colours differential direction displacement distance disturbing force dR dR dt dt Earth elliptically polarized ellipticity equal equation expression extraordinary ray Fcap front function ƒ² glass h²)² Hence inclined integration intensity investigation length longitude mean anomaly Moon motion multiplied nearly node Nutation ordinary ray parallel particles perigee perihelion perpendicular plane of incidence plane of polarization plane of reflection point of Aries principal plane produced PROP proportion quantity radius vector refraction rhombohedron rings shew sin² spheroid Sun's suppose surface tangent tion tourmaline undulation vibration wave