7G TABLE: Decelerate for 48 ¼ Days
To effectively accomplish an interstellar resupply mission, an Artificial Intelligent (AI) vessel could use 7G propulsion to quickly intercept the primary 1G vessel. However, the 7G vessel must slow down prior to intercept in order to match the 1G vessel cruise velocity. This table describes daily progress throughout the deceleration duration.
Previous table, 7G Acceleration for 100 Days, describes daily progress of vessel accelerating from zero velocity at 7g.
After 100 days of 7g acceleration, a vessel travels total distance of 9,842 AUs (.155 Light Year, LY). It gained velocity of about 150 AU/day (.866 c, 86.6% light speed).
Assume 7G vessel cruises at this velocity until the optimal time/distance to start decelerating at 7g.Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

0 days  149.93 AU/dy  86.59% c  9,811.1 AU  0.1551 LY  0.0 AU  9,811.1 AU  27.974% GW_{0}  
1 days  149.46 AU/dy  86.32% c  9,661.7 AU  0.1528 LY  149.4 AU  9,960.5 AU  28.210% GW_{0}  
2 days  148.98 AU/dy  86.04% c  9,512.8 AU  0.1504 LY  148.9 AU  10,109.4 AU  28.445% GW_{0}  
3 days  148.48 AU/dy  85.76% c  9,364.4 AU  0.1481 LY  148.4 AU  10,257.9 AU  28.679% GW_{0}  
4 days  147.98 AU/dy  85.46% c  9,216.5 AU  0.1457 LY  147.9 AU  10,405.8 AU  28.913% GW_{0}  
5 days  147.46 AU/dy  85.17% c  9,069.1 AU  0.1434 LY  147.4 AU  10,553.2 AU  29.146% GW_{0}  
6 days  146.94 AU/dy  84.86% c  8,922.2 AU  0.1411 LY  146.9 AU  10,700.1 AU  29.378% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
For success, the 7G resupply vessel must slow down to match the 1G vessel's cruise velocity (.644c = 111.5 AU/day). This table describes daily progress throughout the 48¼ days of 7G deceleration. 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

7 days  146.40 AU/dy  84.56% c  8,775.8 AU  0.1388 LY  146.4 AU  10,846.5 AU  29.609% GW_{0}  
8 days  145.86 AU/dy  84.24% c  8,630.0 AU  0.1365 LY  145.8 AU  10,992.3 AU  29.840% GW_{0}  
9 days  145.30 AU/dy  83.92% c  8,484.7 AU  0.1342 LY  145.3 AU  11,137.6 AU  30.070% GW_{0}  
10 days  144.73 AU/dy  83.59% c  8,340.0 AU  0.1319 LY  144.7 AU  11,282.3 AU  30.299% GW_{0}  
11 days  144.15 AU/dy  83.26% c  8,195.8 AU  0.1296 LY  144.1 AU  11,426.4 AU  30.527% GW_{0}  
12 days  143.56 AU/dy  82.91% c  8,052.3 AU  0.1273 LY  143.6 AU  11,570.0 AU  30.755% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

13 days  142.96 AU/dy  82.57% c  7,909.3 AU  0.1251 LY  143.0 AU  11,712.9 AU  30.982% GW_{0}  
14 days  142.34 AU/dy  82.21% c  7,767.0 AU  0.1228 LY  142.3 AU  11,855.3 AU  31.208% GW_{0}  
15 days  141.72 AU/dy  81.85% c  7,625.3 AU  0.1206 LY  141.7 AU  11,997.0 AU  31.433% GW_{0}  
16 days  141.08 AU/dy  81.48% c  7,484.2 AU  0.1183 LY  141.1 AU  12,138.1 AU  31.658% GW_{0}  
17 days  140.42 AU/dy  81.10% c  7,343.7 AU  0.1161 LY  140.4 AU  12,278.6 AU  31.881% GW_{0}  
18 days  139.76 AU/dy  80.72% c  7,203.9 AU  0.1139 LY  139.8 AU  12,418.3 AU  32.105% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

19 days  139.08 AU/dy  80.32% c  7,064.8 AU  0.1117 LY  139.1 AU  12,557.5 AU  32.327% GW_{0}  
20 days  138.38 AU/dy  79.92% c  6,926.4 AU  0.1095 LY  138.4 AU  12,695.9 AU  32.549% GW_{0}  
21 days  137.67 AU/dy  79.51% c  6,788.7 AU  0.1073 LY  137.7 AU  12,833.6 AU  32.770% GW_{0}  
22 days  136.95 AU/dy  79.10% c  6,651.7 AU  0.1052 LY  137.0 AU  12,970.6 AU  32.990% GW_{0}  
23 days  136.21 AU/dy  78.67% c  6,515.4 AU  0.1030 LY  136.3 AU  13,106.9 AU  33.210% GW_{0}  
24 days  135.46 AU/dy  78.24% c  6,379.9 AU  0.1009 LY  135.5 AU  13,242.4 AU  33.428% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

25 days  134.70 AU/dy  77.79% c  6,245.1 AU  0.0988 LY  134.8 AU  13,377.2 AU  33.646% GW_{0}  
26 days  133.91 AU/dy  77.34% c  6,111.1 AU  0.0966 LY  134.0 AU  13,511.2 AU  33.864% GW_{0}  
27 days  133.12 AU/dy  76.88% c  5,977.9 AU  0.0945 LY  133.2 AU  13,644.4 AU  34.080% GW_{0}  
28 days  132.30 AU/dy  76.41% c  5,845.5 AU  0.0924 LY  132.4 AU  13,776.8 AU  34.296% GW_{0}  
29 days  131.47 AU/dy  75.93% c  5,713.9 AU  0.0904 LY  131.6 AU  13,908.4 AU  34.512% GW_{0}  
30 days  130.62 AU/dy  75.44% c  5,583.1 AU  0.0883 LY  130.7 AU  14,039.1 AU  34.726% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

31 days  129.76 AU/dy  74.94% c  5,453.2 AU  0.0862 LY  129.9 AU  14,169.0 AU  34.940% GW_{0}  
32 days  128.88 AU/dy  74.43% c  5,324.2 AU  0.0842 LY  129.0 AU  14,298.1 AU  35.153% GW_{0}  
33 days  127.98 AU/dy  73.91% c  5,196.1 AU  0.0822 LY  128.1 AU  14,426.2 AU  35.366% GW_{0}  
34 days  127.06 AU/dy  73.38% c  5,068.9 AU  0.0802 LY  127.2 AU  14,553.4 AU  35.577% GW_{0}  
35 days  126.13 AU/dy  72.84% c  4,942.6 AU  0.0782 LY  126.3 AU  14,679.7 AU  35.788% GW_{0}  
36 days  125.17 AU/dy  72.29% c  4,817.3 AU  0.0762 LY  125.3 AU  14,805.0 AU  35.999% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

37 days  124.20 AU/dy  71.73% c  4,692.9 AU  0.0742 LY  124.4 AU  14,929.4 AU  36.208% GW_{0}  
38 days  123.20 AU/dy  71.15% c  4,569.5 AU  0.0723 LY  123.4 AU  15,052.8 AU  36.417% GW_{0}  
39 days  122.19 AU/dy  70.57% c  4,447.1 AU  0.0703 LY  122.4 AU  15,175.2 AU  36.626% GW_{0}  
40 days  121.15 AU/dy  69.97% c  4,325.7 AU  0.0684 LY  121.4 AU  15,296.6 AU  36.833% GW_{0}  
41 days  120.10 AU/dy  69.36% c  4,205.4 AU  0.0665 LY  120.3 AU  15,416.9 AU  37.040% GW_{0}  
42 days  119.02 AU/dy  68.74% c  4,086.1 AU  0.0646 LY  119.3 AU  15,536.1 AU  37.246% GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

43 days  117.92 AU/dy  68.11% c  3,968.0 AU  0.0627 LY  118.2 AU  15,654.3 AU  37.452%GW_{0}  
44 days  116.80 AU/dy  67.46% c  3,850.9 AU  0.0609LY  117.1 AU  15,771.4 AU  37.657%GW_{0}  
45 days  115.66 AU/dy  66.80%c  3,735.0 AU  0.0591 LY  115.9 AU  15,887.3 AU  37.861%GW_{0}  
46 days  114.49 AU/dy  66.12% c  3,620.2 AU  0.0572 LY  114.8 AU  16,002.1 AU  38.065%GW_{0}  
47 days  113.30 AU/dy  65.44% c  3,506.6 AU  0.0554 LY  113.6 AU  16,115.7 AU  38.268%GW_{0}  
48 days  112.09 AU/dy  64.74% c  3,394.2 AU  0.0537 LY  112.4 AU  16,228.0AU  38.470%GW_{0}  
Resupply Vessel Matches Cruise Velocity of Baseline "Pax" Vessel (1.0 yr of 1G Accel.) at exactly the time/distance of the intercept.  
48¼days  111.78 AU/dy  64.56% c  3,366.3 AU  0.0532 LY  27.9 AU  16,256.0 AU  38.520%GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
Decel. Time(t)  Spot Velocity (V_{t})  Spot Distance (d_{t})  Daily Dist. (d_{Δ})  7G Dist.(d_{7G})  Total Fuel (F)  

52 days  106.98AU/dy  61.79%c  2,966.6 AU  0.2636LY  107.3AU  16,667.7AU  39.272%GW_{0}  
53 days  105.64AU/dy  61.01%c  2,860.5AU  0.2652LY  106.0AU  16,773.7AU  39.471%GW_{0}  
Resupply Vessel Matches Cruise Velocity of Slower "Pax" Vessel (0.9 yr of 1G Accel.) at exactly the time/distance of the intercept.  
53.4 days  105.10AU/dy  60.70%c  2,818.4AU  0.2659LY  42.0 AU  16,815.7AU  39.551%GW_{0}  
54 days  104.27AU/dy  60.22%c  2,755.7AU  0.2662LY  62.6 AU  16,836.3AU  39.669%GW_{0}  
Given 

 d_{t1}  d_{t}  d_{Δ} + Σd_{Δ}  1(1ε∇)^{100+t} 
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