MIX ORBITS

Marsonance T= 1.68 years, Cycler shares same period as Mars, rendezvous with Mars at same orbital position once per orbit. (for more, see "Marsonance"). guaranteed rendezvous with Mars once per Martian orbit.

Terrasonance T=2.00, Earth Resonant cycler.  Same date, every two years, returns to Earth, guaranteed rendezvous with Earth every 2 years.  NOTE:  could add another habitat exactly one year after current one.  Thus, Earth would rendezvous with a habitat once per year.

Synodic Every 2.135 years, Mars and Earth achieve same spatial relationship; thus, Earth dwellers observe Mars in a synodic orbit with period of 2.135 years (about 778 days). NOTE:  Orbit is about 2 1/7 years; thus, after 7 orbits (15 years), habitat would be very close to another quick transport opportunity.  Futhermore, if we added 6 more habitats and evenly spaced all 7 habitats throughout the obit's period; then every synodic orbit a habitat could accomplish quick transport from Earth to Mars.①②③④⑤⑥⑦

①In an ideal situation, habitat will first rendezvous with Earth with Mars leading by about 5°. As habitat continues its orbit past Earth, Mars continues its orbit to its interception point as shown. ②About 65 days later, habitat and Mars both arrive at interception point for another rendezvous.

 

 

Orbital Elements

CONSIDER FOLLOWING:

to be added

	Marsonance			Terrasonance			Synodic
Sidereal Period	TH =	1.878 Yr	Given	TH =	2.000 Yr	Given	TH =	2.135 Yr	Given
Semi-latus Rectum	ℓH =	1.00 AU	Given	ℓH =	1.00 AU	Given	ℓH =	1.00 AU	Given
Semi-major axis	aH =	1.522 AU	=  ∛(T2)	aH =	1.587 AU	=  ∛(T2)	a♂ =	1.658 AU	=  ∛(T2)
Semi-minor axis	bH =	1.234 AU	= √(ℓ × a)	bH =	1.260 AU	= √(ℓ × a)	b♂ =	1.288 AU	= √(ℓ × a)
Focus	cH =	0.892 AU	= √(a2 - b2)	cH =	0.966 AU	= √(a2 - b2)	c♂ =	1.045 AU	=  √(a2 - b2)
Eccentricity	eH =	0.586	= c / a	eH =	0.608	= c / a	e♂ =	0.630	= c / a
Perihelion	RMin = qH =	0.631 AU	see below	RMin = qH =	0.622 AU	see below	RMin = qH =	0.614 AU	see below
Aphelion	RMax = QH =	2.414 AU	see below	RMax = QH =	2.553 AU	see below	RMax = QH =	2.703 AU	see below
Max Velocity	VMax =	47.4 kps	see below	VMax =	48.0 kps	see below	VMax =	48.7 kps	see below
Min Velocity	VMin  =	12.4 kps	see below	VMin =	11.7 kps	see below	VMin =	11.1 kps	see below

Earth Resonance

Period (T)	Semi-Major Axis (a)
2 Years	∛(T2) = 1.587 AU

Semilatus Rectum	Semiminor Axis	Focus	Eccen- tricity	Perihelion	Aphelion	Max Velocity	Min Velocity
ℓ	b	c	e	RMin = q θ=0°	RMax = Q θ=180°	VMax θ=0°	VMin θ=180°
0.5 AU	0.891 AU	1.314 AU	0.828	0.274 AU	2.901 AU	77.19 kps	7.28 kps
1 AU	1.260 AU	0.966 AU	0.608	0.622 AU	2.553 AU	48.03 kps	11.70 kps
1.5 AU	1.543 AU	0.372 AU	0.235	1.215 AU	1.960 AU	30.10 kps	18.66 kps
Given	√(ℓ × a)	√(a2 - b2)	c ÷ a	ℓ (1 + e × Cos(θ))		√(μSol( 2 R - 1 a ))
1 AU	1.260 AU	0.966 AU	0.608	0.622 AU	2.553 AU	48.03 kps	11.70 kps
1.37 AU	1.475 AU	0.587 AU	0.370	1.00 AU	2.175AU	34.96 kps	16.07 kps
b2 ÷ a	√(a2 - c2)	a - q	c ÷ a	Given	a + c	√(μSol( 2 R - 1 a ))
ℓ	b	c	e	q	Q	VMax θ=0°	VMin θ=180

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μSol = 891.906 AU-km2 / sec2 √μSol = 29.865 AU-km / sec Rθ = ℓH 1 + eH × Cos(θ) Position qH = RMin = ℓH 1 + eH × Cos(0°) QH = RMax = ℓH 1 + eH × Cos(180°) Vθ =√(μSol( 2 Rθ - ℓ aH ) )  Velocity VMax =√( 2μSol q - ℓ × μSol aH ) VMin =√( 2μSol Q - ℓ × μSol aH )

Cycler Relevant Positions

Pos.	Time	Range	Cycler Velocity
ν	Days	AU	km/sec
0°	0	0.614 AU	48.6
90°	50	1.000 AU	35.2
127°	112	1.611 AU	23.8
180°	392	2.703 AU	11.02
Given	Deg	AU	km/sec

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Semimajor Axis(a)
Given: a = 1.58 AU
Perihelion (q)
q = a - c
    Focus (c)
c = a - q
    c² = a² -2aq + q²  
Semiminor Axis (b)
b² = a² - c²  
b² = 2aq - q²  = q (2a - q)
b = √(q (2a - q))
Semi Latis Rectum (ℓ)
ℓ  = b² / a

q	b	ℓ
(AU)	(AU)	(AU)
0.1	0.55	0.19
0.2	0.77	0.37
0.3	0.93	0.54
0.4	1.05	0.70
0.5	1.15	0.84
0.6	1.24	0.97
0.7	1.31	1.09
0.8	1.37	1.19
0.9	1.43	1.29
1	1.47	1.37

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√(μSol(

2 R

-

ℓ a

))