Expression 12: "M" Subscript, "S" "S" "T" "O" , Baseline equals "e" Superscript, StartFraction, "V" Subscript, 0 , Baseline Over "I" Subscript, "s" "p" , Baseline times 9.8 1 , EndFraction , Baseline times left parenthesis, "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline plus "m" Subscript, "d" "r" "y" , Baseline , right parenthesis minus "m" Subscript, "d" "r" "y" , Baseline minus "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , BaselineMSSTO=eV0Isp·9.81·mpayload+mdry−mdry−mpayload
equals=
712.5 1 7 0 6 4 2 1 4712.517064214
12
Expression 13: "x" equals "M" Subscript, 2 "S" "t" "a" "g" "e" , Baselinex=M2Stage
equals=
572.5 6 2 9 5 1 4 6 2572.562951462
13
Expression 14: "M" Subscript, 2 "S" "t" "a" "g" "e" , Baseline equals "e" Superscript, StartFraction, "V" Subscript, 0 , Baseline Over "I" Subscript, "s" "p" , Baseline times 9.8 1 , EndFraction , Baseline times left parenthesis, "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline plus StartFraction, left parenthesis, "V" Subscript, 0 , Baseline minus "f" left parenthesis, "b" , right parenthesis , right parenthesis times "m" Subscript, "d" "r" "y" , Baseline Over "V" Subscript, 0 , Baseline , EndFraction , right parenthesis minus StartFraction, left parenthesis, "V" Subscript, 0 , Baseline minus "f" left parenthesis, "b" , right parenthesis , right parenthesis times "m" Subscript, "d" "r" "y" , Baseline Over "V" Subscript, 0 , Baseline , EndFraction minus "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline plus "b" plus "c"M2Stage=eV0Isp·9.81·mpayload+V0−fb·mdryV0−V0−fb·mdryV0−mpayload+b+c
equals=
572.5 6 2 9 5 1 4 6 2572.562951462
14
Expression 15: "f" left parenthesis, "x" , right parenthesis equals "I" Subscript, "s" "p" , Baseline times 9.8 1 times natural log left parenthesis, StartFraction, "m" Subscript, "d" "r" "y" , Baseline plus "x" plus "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline Over "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline plus "m" Subscript, "d" "r" "y" , Baseline , EndFraction , right parenthesisfx=Isp·9.81·lnmdry+x+mpayloadmpayload+mdry
15
Expression 16: "g" left parenthesis, "x" , right parenthesis equals "I" Subscript, "s" "p" , Baseline times 9.8 1 times natural log left parenthesis, StartFraction, StartNestedFraction, left parenthesis, "V" Subscript, 0 , Baseline minus "f" left parenthesis, "b" , right parenthesis , right parenthesis times "m" Subscript, "d" "r" "y" , Baseline NestedOver "V" Subscript, 0 , Baseline , EndNestedFraction plus left parenthesis, "x" minus "b" minus "c" , right parenthesis plus "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline Over "m" Subscript, "p" "a" "y" "l" "o" "a" "d" , Baseline plus StartNestedFraction, left parenthesis, "V" Subscript, 0 , Baseline minus "f" left parenthesis, "b" , right parenthesis , right parenthesis times "m" Subscript, "d" "r" "y" , Baseline NestedOver "V" Subscript, 0 , Baseline , EndNestedFraction , EndFraction , right parenthesisgx=Isp·9.81·lnV0−fb·mdryV0+x−b−c+mpayloadmpayload+V0−fb·mdryV0
16
Label: left parenthesis, "M" Subscript, "S" "S" "T" "O" , Baseline , "f" left parenthesis, "M" Subscript, "S" "S" "T" "O" , Baseline , right parenthesis , right parenthesisMSSTO,fMSSTO
Label:
equals=
left parenthesis, 712.5 1 7 0 6 4 , 9500 , right parenthesis712.517064,9500
17
Label: left parenthesis, "M" Subscript, 2 "S" "t" "a" "g" "e" , Baseline , "g" left parenthesis, "M" Subscript, 2 "S" "t" "a" "g" "e" , Baseline , right parenthesis , right parenthesisM2Stage,gM2Stage
Label:
equals=
left parenthesis, 572.5 6 2 9 5 1 , 9500 , right parenthesis572.562951,9500
18
Label: left parenthesis, "b" , "f" left parenthesis, "b" , right parenthesis , right parenthesisb,fb
Label:
equals=
left parenthesis, 120 , 4487.8 5 0 7 4 , right parenthesis120,4487.85074
19
20
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powered by
left parenthesis, 712.5 1 7 0 6 , 9500 , right parenthesis712.51706,9500
left parenthesis, 572.5 6 2 9 5 , 9500 , right parenthesis572.56295,9500
left parenthesis, 120 , 4487.8 5 0 7 4 , right parenthesis120,4487.85074