Expression 10: "u" Subscript, "p" "d" "a" "t" "e" , Baseline equals alpha to left bracket, mod left parenthesis, alpha left bracket, "i" , right bracket plus StartFraction, 10 Superscript, negative "p" , Baseline Over "d" left parenthesis, alpha left bracket, "i" , right bracket , "a" left bracket, "i" , right bracket , "E" Subscript, "c" "c" , Baseline left bracket, "i" , right bracket , right parenthesis squared , EndFraction , 2 pi , right parenthesis for "i" equals left bracket, 1 , ... , "p" Subscript, "l" "a" "n" "e" "t" "s" , Baseline , right bracket , right bracketupdate=α→modαi+10−pdαi,ai,Ecci2,2πfori=1,...,planets
10
Expression 11: "p" Subscript, "l" "a" "n" "e" "t" "s" , Baseline equals min left parenthesis, "a" .length , "E" Subscript, "c" "c" , Baseline .length , phi .length , alpha . , right parenthesisplanets=mina.length,Ecc.length,ϕ.length,α.length
equals=
55
11
Expression 12: "p" equals 1p=1
11
55
12
Hidden Label: left parenthesis, cos left parenthesis, alpha plus phi , right parenthesis , sin left parenthesis, alpha plus phi , right parenthesis , right parenthesis "d" left parenthesis, alpha , "a" , "E" Subscript, "c" "c" , Baseline , right parenthesiscosα+ϕ,sinα+ϕdα,a,Ecc
Label
equals=
left parenthesis, 0.2 1 8 1 , negative 0.8 3 0 9 , right parenthesis0.2181,−0.8309
left parenthesis, 1.4 3 9 , negative 1.3 6 8 , right parenthesis1.439,−1.368
left parenthesis, negative 10.9 6 , 0.5 2 9 7 , right parenthesis−10.96,0.5297
left parenthesis, 1.7 7 5 , negative 6.2 5 3 , right parenthesis1.775,−6.253
left parenthesis, negative 5.1 7 2 , 0.0 7 6 4 3 , right parenthesis−5.172,0.07643
13
Expression 14: "r" equals "d" left parenthesis, theta minus phi , "a" , "E" Subscript, "c" "c" , Baseline , right parenthesisr=dθ−ϕ,a,Ecc
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
2 pi2π
domain \theta Maximum:
14
Hidden Label: left parenthesis, cos left parenthesis, phi , right parenthesis , sin left parenthesis, phi , right parenthesis , right parenthesis "d" left parenthesis, 0 , "a" , "E" Subscript, "c" "c" , Baseline , right parenthesiscosϕ,sinϕd0,a,Ecc
Label
equals=
left parenthesis, 1.5 , 0 , right parenthesis1.5,0
left parenthesis, 1.5 5 6 , 1.5 5 6 , right parenthesis1.556,1.556
left parenthesis, negative 11.2 9 , 1.6 0 9 , right parenthesis−11.29,1.609
left parenthesis, 1.8 4 4 , negative 6.2 3 3 , right parenthesis1.844,−6.233
left parenthesis, negative 2.2 8 9 , 5.0 0 1 , right parenthesis−2.289,5.001
15
Hidden Label: left parenthesis, cos left parenthesis, pi plus phi , right parenthesis , sin left parenthesis, pi plus phi , right parenthesis , right parenthesis "d" left parenthesis, pi , "a" , "E" Subscript, "c" "c" , Baseline , right parenthesiscosπ+ϕ,sinπ+ϕdπ,a,Ecc
Label
equals=
left parenthesis, negative 0.5 , 0 , right parenthesis−0.5,0
left parenthesis, negative 1.2 7 3 , negative 1.2 7 3 , right parenthesis−1.273,−1.273
left parenthesis, 0.5 9 4 , negative 0.0 8 4 6 7 , right parenthesis0.594,−0.08467
left parenthesis, negative 0.9 9 2 8 , 3.3 5 6 , right parenthesis−0.9928,3.356
left parenthesis, 1.8 7 3 , negative 4.0 9 2 , right parenthesis1.873,−4.092
