Ths sheet has three parts:1. The brachistochrone calculator. This, if it works, will take distance, thrust, intial mass, and mass flow, and give time and deltaV for a brachistochrone.If it doesn't work, then try to use solver manually. Have it bring Ddif (B82) to 0 by altering Ta (B71)2. This gives you position, velocity, mass, and acceleration for a given time, given initial mass, mass flow, and thrust.3. Does the same as 2, but graphs for the quantities, using 100 subintervals. If you want the raw numbers, then scroll down.

1. The brachistochrone calculator. This, if it works, will take distance, thrust, intial mass, and mass flow, and give time and deltaV for a brachistochrone.

2. This gives you position, velocity, mass, and acceleration for a given time, given initial mass, mass flow, and thrust.3. Does the same as 2, but graphs for the quantities, using 100 subintervals. If you want the raw numbers, then scroll down.

Distance (m) 4.00E+08 Acceleration Time (S) 15397.19

Initial Mass (kg.) 917225 Deceleration Time (S) 13905.83

Mass Flow (kg/s) 5.77 Total Time (S) 29303.02

Thrust (N) 1966182 Delta-V (m/s) 69431.06

Remass (kg.) 169078.4

Va 34715.528Ta 15397.189Xa 262723614Xd 237276386VaC -4678323Vdp 34715.528Td 13905.828Mt 828383.22Vf -6.286E-07VdC -4643608Vda 34715.528Dt 500000000Ddif -1E+08XaC -6.9E+11mi-mfTa 828383.22mt-mfTd 748146.59XdC -6.18E+11

Initial Mass (kg.) 917225 Acceleration (m/s2) 2.3735174

Mass Flow (kg/s) 5.77 Velocity (m/s) 34715.528

Thrust (N) 1966182 Position (m) 262723614

Time (s) 15397.189 Remass (kg.) 88841.782

Va 34715.528Xa 262723614VaC -4678323XaC -6.9E+11mi-mfTa 828383.22

Initial Mass (kg.) 917225

Mass Flow (kg/s) 5.77

Thrust (N) 1966182

Final Time (s) 28800

0 5000 10000 15000 20000 25000 30000 35000

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Acceleration

Seconds

m/s2

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Velocity

Seconds

m/s

VaC -4678323XaC -6.9E+11

Tstep T Acceleration Velocity Position0 0 2.14362015863065 0 0

0.01 288 2.14751085899866 617.92253 88953.950.02 576 2.1514157083978 1236.9676 356031.10.03 864 2.15533478415082 1857.1393 801555.50.04 1152 2.15926816414489 2478.4418 14258520.05 1440 2.16321592683682 3100.8792 22292470.06 1728 2.16717815125821 3724.4556 32120680.07 2016 2.17115491702075 4349.1752 43746430.08 2304 2.17514630432157 4975.0422 57173030.09 2592 2.17915239394861 5602.0609 7240378

0.1 2880 2.18317326728606 6230.2354 89442010.11 3168 2.18720900631989 6859.5701 108291050.12 3456 2.19125969364344 7490.0692 128954250.13 3744 2.19532541246302 8121.7371 151434970.14 4032 2.1994062466036 8754.5781 175736580.15 4320 2.20350228051462 9388.5966 201862470.16 4608 2.20761359927577 10023.797 229816030.17 4896 2.21174028860292 10660.184 259600680.18 5184 2.21588243485402 11297.761 291219830.19 5472 2.22004012503518 11936.533 32467693

0.2 5760 2.22421344680674 12576.505 359975420.21 6048 2.22840248848943 13217.682 397118760.22 6336 2.2326073390706 13860.067 436110420.23 6624 2.23682808821051 14503.665 476953910.24 6912 2.24106482624875 15148.481 519652700.25 7200 2.24531764421062 15794.52 564210330.26 7488 2.24958663381369 16441.786 610630320.27 7776 2.25387188747439 17090.283 658916200.28 8064 2.25817349831466 17740.018 709071540.29 8352 2.26249156016872 18390.993 76109989

0.3 8640 2.26682616758988 19043.214 815004850.31 8928 2.27117741585743 19696.686 870790010.32 9216 2.27554540098366 20351.414 92845897

0.33 9504 2.27993021972087 21007.402 988015360.34 9792 2.28433196956854 21664.656 1.05E+080.35 10080 2.28875074878059 22323.179 1.11E+080.36 10368 2.29318665637262 22982.978 1.18E+080.37 10656 2.29763979212936 23644.056 1.25E+080.38 10944 2.30211025661212 24306.42 1.31E+080.39 11232 2.30659815116641 24970.073 1.39E+08

0.4 11520 2.31110357792952 25635.022 1.46E+080.41 11808 2.31562663983835 26301.271 1.53E+080.42 12096 2.32016744063718 26968.825 1.61E+080.43 12384 2.32472608488565 27637.689 1.69E+080.44 12672 2.32930267796677 28307.869 1.77E+080.45 12960 2.33389732609504 28979.369 1.85E+080.46 13248 2.33851013632466 29652.195 1.94E+080.47 13536 2.34314121655785 30326.353 2.02E+080.48 13824 2.34779067555328 31001.846 2.11E+080.49 14112 2.35245862293454 31678.682 2.2E+08

0.5 14400 2.35714516919882 32356.864 2.29E+080.51 14688 2.36185042572558 33036.399 2.39E+080.52 14976 2.36657450478536 33717.292 2.48E+080.53 15264 2.37131751954877 34399.548 2.58E+080.54 15552 2.3760795840955 35083.173 2.68E+080.55 15840 2.38086081342342 35768.172 2.78E+080.56 16128 2.38566132345792 36454.55 2.89E+080.57 16416 2.3904812310612 37142.314 2.99E+080.58 16704 2.39532065404182 37831.469 3.1E+080.59 16992 2.40017971116426 38522.021 3.21E+08

0.6 17280 2.40505852215862 39213.975 3.32E+080.61 17568 2.40995720773051 39907.337 3.44E+080.62 17856 2.41487588957095 40602.112 3.55E+080.63 18144 2.41981469036648 41298.307 3.67E+080.64 18432 2.42477373380935 41995.927 3.79E+080.65 18720 2.42975314460784 42694.979 3.91E+080.66 19008 2.43475304849673 43395.467 4.04E+080.67 19296 2.43977357224786 44097.398 4.16E+080.68 19584 2.44481484368087 44800.779 4.29E+080.69 19872 2.44987699167403 45505.614 4.42E+08

0.7 20160 2.45496014617522 46211.91 4.55E+080.71 20448 2.46006443821308 46919.673 4.69E+080.72 20736 2.46518999990822 47628.909 4.82E+080.73 21024 2.47033696448467 48339.624 4.96E+080.74 21312 2.47550546628137 49051.825 5.1E+080.75 21600 2.48069564076392 49765.518 5.24E+080.76 21888 2.48590762453636 50480.708 5.39E+080.77 22176 2.49114155535319 51197.402 5.53E+080.78 22464 2.49639757213147 51915.608 5.68E+080.79 22752 2.50167581496316 52635.33 5.83E+08

0.8 23040 2.50697642512752 53356.575 5.99E+080.81 23328 2.51229954510377 54079.35 6.14E+080.82 23616 2.51764531858377 54803.662 6.3E+080.83 23904 2.52301389048505 55529.516 6.46E+08

0.84 24192 2.52840540696383 56256.92 6.62E+080.85 24480 2.53382001542832 56985.88 6.78E+080.86 24768 2.53925786455215 57716.402 6.95E+080.87 25056 2.54471910428795 58448.495 7.11E+080.88 25344 2.55020388588118 59182.163 7.28E+080.89 25632 2.55571236188407 59917.414 7.45E+08

0.9 25920 2.56124468616975 60654.255 7.63E+080.91 26208 2.5668010139466 61392.694 7.8E+080.92 26496 2.57238150177274 62132.735 7.98E+080.93 26784 2.57798630757077 62874.388 8.16E+080.94 27072 2.58361559064264 63617.658 8.34E+080.95 27360 2.58926951168474 64362.553 8.53E+080.96 27648 2.59494823280322 65109.079 8.71E+080.97 27936 2.60065191752945 65857.245 8.9E+080.98 28224 2.60638073083574 66607.057 9.09E+080.99 28512 2.61213483915123 67358.523 9.29E+08

1 28800 2.61791441037802 68111.649 9.48E+08

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m/s2

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Seconds

m/s

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0100000000200000000300000000400000000500000000600000000700000000800000000900000000

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Displacement

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m

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0100000200000300000400000500000600000700000800000900000

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Mass

Seconds

kg.

Mass917225

915563.2913901.5912239.7

910578908916.2907254.4905592.7903930.9902269.2900607.4898945.6897283.9895622.1893960.4892298.6890636.8888975.1887313.3885651.6883989.8

882328880666.3879004.5877342.8

875681874019.2872357.5870695.7

869034867372.2865710.4864048.7

862386.9860725.2859063.4857401.6855739.9854078.1852416.4850754.6849092.8847431.1845769.3844107.6842445.8

840784839122.3837460.5835798.8

834137832475.2830813.5829151.7

827490825828.2824166.4822504.7820842.9819181.2817519.4815857.6814195.9812534.1810872.4809210.6807548.8805887.1804225.3802563.6800901.8

799240797578.3795916.5794254.8

792593790931.2789269.5787607.7

785946784284.2782622.4780960.7779298.9

777637.2775975.4774313.6772651.9770990.1769328.4767666.6766004.8764343.1762681.3761019.6759357.8

757696756034.3754372.5752710.8

751049