SNOWBALL FROM OORT
RESUPPLY MISSIONS.
During the several years that interstellar vessels must "cruise" between stars, new provisions from the Oort Cloud could be put to good use
Oort Cloud (OC) is a huge, spherical body of comets orbiting Sol from 0.3 lightyear (LY) to beyond an entire LY. It is the most likely source of most longperiod comets. For more on Oort Cloud.

After 1 year (365 days) of 1g acceleration, TE's interstellar vessel crew decides to stop propulsion due to fuel concerns. Vessel will maintain constant velocity of 64.4% light speed for several years. Vessel's distance can be described by following equation; d_{1G} = A_{365} + V_{1G} × t = .377 LY + .644c × t  After 1g vessel accelerates for 265.25 days, 7g vessel initiates 100 days of 7g acceleration. Thus, both vessels start their respective constant velocities around the time the 1g vessel completes the one year acceleration. 7g vessel maintains constant .866c for a certain duration. Vessel's distance can be described as follows:
d_{7G} = A_{100} + V_{7G} × t = .155 LY + .866c × t
 
AT CONSTANT VELOCITY, vessels intercept as shown.
For first year, both 1g passenger vessel and the resupply 7g vessel go through their respective acceleration profiles as described above. Throughout 2nd year, both vessels cruise on the same path to the same destination star at their respective constant velocities. The 1g pax vessel is .377 LY (23,841.5 AU) from Sol with velocity of .644 c (= 111.5 AU/day = 193,066 km/sec). The 7g resupply vessel is much closer to Sol .155 LY (9,802 AU) from Sol with much greater velocity, .866 c (= 149.9 AU/day = 259,620 km/sec); thus, the resupply vessel will inevitably overtake the pax vessel.Compute point of interception via common solution to above linear equations:
Unfortunately, there is a huge velocity differential between the two vessels
For the two vessels to rendezvous, their velocity must be equal at the point of interception; thus, the resupply vessel must decelerate prior to meeting pax vessel..866c .644c = .222c = 38.44 AU/day = 66,554 km/sec  
Deceleration requires following adjustments to Resupply Vessel Profile: Linear programming method starts with desired end point; then, work backward to determine required start point.  

7G's Deceleration Endpoint
must match 1G vessel's velocity at predetermined intercept.
7G resupply vessel must decelerate from 149.9 AU to match 1G pax vessel's velocity (111.8 AU/day) exactly at an intercept point. Arbitrarily chose an intercept point of 2.0 years and 64,824 AU after 1G vessel launch.
 
ADJUST ENDPOINTS OF 7G CRUISE
ⓐ 360.2 Days. Change 7G cruise start from 365.25 days. Cruise velocity remains 149.9 AU/day; thus, the 7G acceleration duration must also remain 100 days. To accommodate the shifted acceleration 100 day duration (see below), 7g cruise distance has new ordinate intercept (Y_{O}):
d_{AU} = 44,986 AU + t_{Dy}×149.9 AU/day
ⓑ 365.25 Days (remains the same). Stop 1G acceleration; start 1G cruise; velocity = 111.5 AU/day as described above.
ⓒ 400 days: Resupply vessel lags pax vessel by 11,982 AU.
ⓓ 500 days: Due to much greater speed, resupply vessel shortens the lag to 8,142 AU.
ⓔ 600 days: The lag is further shortened to 4,302 AU.
ⓕ 684 days: When resupply vessel reaches 1,076 AU behind the pax vessel, it prepares to decelerate. Cruise segment ends at point where deceleration starts.
 
7G Resupply Vessel Shifts Acceleration Period.
① t = 0.0 days. Initiate acceleration of 1g vessel for passengers ("pax").
② t = 260.2 days. 7G resupply vessel launches and accelerates. This 5 day adjustment proves necessary to eventually intercept the pax vessel in two years past point ①.
③ t = 360.2 days. 7g vessel stops acceleration and starts constant velocity, a linear function. For more details, click: 7G Acc
④ t = 365.25 days. 1g vessel stops acceleration and starts constant velocity. For more details, click: 1G Acc
 
Resupply Mission Ends
With 1 G Deceleration
Traditional 1G Profile: Pax vessel initially accelerates at 1G for one year to attain velocity of 64.43c over a distance of .38 LY. After an indeterminate cruise duration (most likely several years), pax vessel must decelerate for same time/distance just prior to destination.
Resupply 1G Profile starts the same as traditional profile. However, it differs when pax vessel is joined by resupply vessel which partially decelerates from much higher velocity to match pax vessel's cruise speed. Finally, the pax and resupply vessel decelerate in tandem just prior to destination. For more, click: 1G Dec

 

7G Total Fuel Consumption is 49.1% of vessel's initial Gross Weight (GW_{0}) after following power profile:
1) 100 days 7G acceleration to high speed cruise.
2) 48¼ days 7G deceleration to rendezvous with 1G Pax vessel.
3) 365¼ days 1G deceleration in tandem with Pax vessel to orbit at destination.
For more, see More Snowalls. 
VOLUME I: ASTEROIDAL 

VOLUME II: INTERPLANETARY 
VOLUME III: INTERSTELLAR 
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