The Elliptical Orbit

Orbital Paths

Expression 19: 1 equals StartFraction, "x" squared Over "a" squared , EndFraction plus StartFraction, "y" squared Over "b" squared , EndFraction

Expression 20: 1 equals StartFraction, "x" squared plus 11 Over "a" squared , EndFraction plus StartFraction, "y" squared plus 50 Over .6 "b" squared , EndFraction

Expression 21: 1 equals StartFraction, "x" squared plus 10 Over "a" squared , EndFraction plus StartFraction, "y" squared plus 10 Over "b" squared , EndFraction

Rotational Around Center (External)

Expression 23: "d" Subscript, "e" "g" "r" "e" "e" "O" "f" "R" "o" "t" "a" "t" "i" "o" "n" , Baseline equals 199.1

360

Expression 24: "s" equals StartFraction, negative "d" Subscript, "e" "g" "r" "e" "e" "O" "f" "R" "o" "t" "a" "t" "i" "o" "n" , Baseline pi Over 180 , EndFraction

equals

negative 3.4 5 9 2 4 2 5 7 7 4 5

Imaginary Stick

"x" Subscript, 1 , Baseline	"y" Subscript, 1 , Baseline
"m"	"n"	r1c3:
"w"	"z"	r2c3:
		r3c3:

Circle for the Moon

Expression 28: left parenthesis, "x" minus "a" left parenthesis, cos "s" , right parenthesis , right parenthesis squared plus left parenthesis, "y" minus "b" left parenthesis, sin "s" , right parenthesis , right parenthesis squared equals 1

"x" Subscript, 2 , Baseline	"y" Subscript, 2 , Baseline
"u"	"v"	r1c3:
"c"	"d"	r2c3:
"j"	"k"	r3c3:
"u"	"v"	r4c3:
		r5c3:

Rotation around Axis (Internal)

Expression 31: "d" Subscript, 1 "e" "g" "r" "e" "e" "O" "f" "R" "o" "t" "a" "t" "i" "o" "n" , Baseline equals 180

negative 360

360

Expression 32: "t" equals StartFraction, "d" Subscript, 1 "e" "g" "r" "e" "e" "O" "f" "R" "o" "t" "a" "t" "i" "o" "n" , Baseline pi Over 180 , EndFraction

equals

3.1 4 1 5 9 2 6 5 3 5 9

Elliptical Shape

Expression 34: "a" equals 19.6

Expression 35: "b" equals 10