### EARTH's ELLIPTICITY Helps a Lot!!!

**Recall Kepler's Third Law**: The square of an object's orbital period (

**T²**) is proportional to the cube of the semi-major axis (

**a³**) of its orbit.Thus, all Solar orbiting objects can relate to each other as follows:

**T**

_{1}² / a_{1}³ = T_{2}² / a_{2}³####
Let **T**_{1 }= 365.25 days = 1 year

**T**

_{1 }= 365.25 days = 1 year####
**a**_{1}_{ }= 149,700,000 km = 1.0 AU (Earth's actual observed elliptical orbit semimajor axis, a)

_{1}

_{ }= 149,700,000 km = 1.0 AU (Earth's actual observed elliptical orbit semimajor axis, a)

####
**a**_{2}_{ }= **147,300,000 km = 0.98397 AU ****(a for an artificial circular orbit with Earth's perihelion as radius)**

_{2}

_{ }=

####
**Solve for T**_{2 }**= √ a**_{2}³ **= √ ****0.98397****³ ****= ****.976 year = 356.5 days**

_{2 }

_{2}³

**SUMMARY:**Many experts propose Lagrange points, L-4 (60° before Earth) and L-5 (60° behind Earth) as optimal parking spots for such Habitats, which TE calls Habitat-Alpha (Hab-α) and Habitat-Omega (Hab-Ω) respectively. Use following methods to properly place Habitats into Earth's Solar Orbit.

**Enter Circular Orbit:**On about Jan. 3, Earth arrives at its perihelion (orbit's nearest point to Sol); thus, this is a great position for Hab-α to enter a circular orbit with shorter semi-major axis and thus reach L-4 in about 6½ years (without this circular orbit, it would take about 40+ years to reach L-4). Alternatively, Earth arrives at aphelion (farthest from Sol) on about July 4; thus, a great position for Hab-Ω to enter a circular orbit with larger semi-major axis to reach L-5 in about 7 years.

**Park at L4/L5:**Final burn needed by each Habitat when they each reach designated parking spot; perhaps provided by a space tug.

**CONCLUSION:**7 years travel time is much better than 40 years travel discussed in previous chapter attained by Lunar Launches from either Full Moon or New Moon.

**TRANSITION:**

**HOWEVER, we can do even better. Properly oriented cycler orbits can reduce travel time to two years or even less, discussed in next chapter, Leveraging Lamba.**

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