THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
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Fig. 2. 
Let X, Y, Z be a second set of rectangular axes, XY being the plane of Diana’s 
orbit. 
Let M be the projection of Diana in her orbit. 
Let i=ZC, the obliquity of the equator to the plane of Diana’s orbit. 
X =AX=BCY. 
1 = MX, Diana’s longitude from the node X. 
Let M, = cos MAh 
M 2 = cos MB > Diana’s direction-cosines referred to A, B, C. 
M ?j = cos MC J 
Then 
M x = cos l, cos X/ + sin sin x, cos i t j 
M,= — cos l t sin y + sin l cos X/ cos iV .(19) 
Mo = sin l t sin i / J 
We may observe that M 3 is derivable from M x by writing Xx+i 77 " i n place of x,- 
These expressions refer to the plane of Diana’s orbit, but we must now refer to the 
ecliptic. 
Fig\ 3. 
In fig. 3, let A be the autumnal equinox, B the ascending node of the orbit, C the 
intersection of the orbit with the equator, being the X of fig. 2, and let D be a point 
fixed in the equator, being the A of fig. 2. 
Then if we refer to the sides and angles of the spherical triangle A B C by the letters 
a, b, c, A, B, C as is usual in works on spherical trigonometry, we have 
A =i, the obliquity of the ecliptic. 
B =j, the inclination of the orbit. 
tt — C = q=ZC of fig. 2. 
c =iY, the longitude of the node measured from A, for at present we may 
suppose i/>=0, without loss of generality. 
