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Review speed of Earth around Sun

step inference rule input feed output step validity (as per SymPy)
1
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 5426308937
    \(v = \frac{d}{t}\)
 no validation is available for declarations
2
  • 0000111886: change variable X to Y
  • number of inputs: 1; feeds: 2; outputs: 1
  • Change variable $#1$ to $#2$ in Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.
  1. 5426308937
    \(v = \frac{d}{t}\)
  1. 7476820482
    \(C\)
  2. 1277713901
    \(d\)
  1. 6946088325
    \(v = \frac{C}{t}\)
 LHS diff is 0 RHS diff is (pdg0001943 - pdg0003034)/pdg0001467
Note about step 3: circumference of a circle
3
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 6785303857
    \(C = 2 \pi r\)
 no validation is available for declarations
4
  • 0000111984: change two variables in expression
  • number of inputs: 1; feeds: 4; outputs: 1
  • Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.
  1. 6785303857
    \(C = 2 \pi r\)
  1. 4202292449
    \(r_{\rm Earth\ orbit}\)
  2. 2346150725
    \(r\)
  3. 6239815585
    \(C_{\rm Earth\ orbit}\)
  4. 9306496484
    \(C\)
  1. 6348260313
    \(C_{\rm Earth\ orbit} = 2 \pi r_{\rm Earth\ orbit}\)
 LHS diff is -pdg0001534 + pdg0003034 RHS diff is 2*pdg0003141*(pdg0002530 - pdg0006081)
5
  • 0000111236: change three variables in expression
  • number of inputs: 1; feeds: 6; outputs: 1
  • Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\ref{eq:#7}; yields Eq.~\ref{eq:#8}.
  1. 6946088325
    \(v = \frac{C}{t}\)
  1. 4470433702
    \(t_{\rm Earth\ orbit}\)
  2. 8135396036
    \(t\)
  3. 9601500174
    \(v_{\rm Earth\ orbit}\)
  4. 9753878784
    \(v\)
  5. 7708501762
    \(C_{\rm Earth\ orbit}\)
  6. 4057686137
    \(C\)
  1. 3046191961
    \(v_{\rm Earth\ orbit} = \frac{C_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}}\)
 LHS diff is pdg0001357 - pdg0007427 RHS diff is -pdg0001534/pdg0005344 + pdg0003034/pdg0001467
6
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 3046191961
    \(v_{\rm Earth\ orbit} = \frac{C_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}}\)
  2. 6348260313
    \(C_{\rm Earth\ orbit} = 2 \pi r_{\rm Earth\ orbit}\)
  1. 3080027960
    \(v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}}\)
 LHS diff is pdg0001534 - pdg0007427 RHS diff is 2*pdg0003141*pdg0006081*(pdg0005344 - 1)/pdg0005344
7
  • 0000111104: declare assumption
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an assumption.
  1. 7175416299
    \(t_{\rm Earth\ orbit} = 1 {\rm year}\)
 no validation is available for declarations
8
  • 0000111646: multiply RHS by unity
  • number of inputs: 1; feeds: 1; outputs: 1
  • Multiply RHS of Eq.~\ref{eq:#2} by 1, which in this case is $#1$; yields Eq.~\ref{eq:#3}
  1. 7175416299
    \(t_{\rm Earth\ orbit} = 1 {\rm year}\)
  1. 3219318145
    \(\frac{365 {\rm days}}{1 {\rm year}} \frac{24 {\rm hours}}{1 {\rm day}} \frac{60 {\rm minutes}}{1 {\rm hour}} \frac{60 {\rm seconds}}{1 {\rm minute}}\)
  1. 8721295221
    \(t_{\rm Earth\ orbit} = 3.16 10^7 {\rm seconds}\)
 feed diff is 364 LHS diff is 0 RHS diff is 362
9
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 3080027960
    \(v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}}\)
  2. 8721295221
    \(t_{\rm Earth\ orbit} = 3.16 10^7 {\rm seconds}\)
  1. 4593428198
    \(v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{3.16\ 10^7 {\rm seconds}}\)
 LHS diff is pdg0005344 - pdg0007427 RHS diff is -0.632911392405063*pdg0003141*pdg0006081 + 3
10
  • 0000111104: declare assumption
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an assumption.
  1. 3472836147
    \(r_{\rm Earth\ orbit} = 1.496\ 10^8 {\rm km}\)
 no validation is available for declarations
11
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 4593428198
    \(v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{3.16\ 10^7 {\rm seconds}}\)
  2. 3472836147
    \(r_{\rm Earth\ orbit} = 1.496\ 10^8 {\rm km}\)
  1. 6998364753
    \(v_{\rm Earth\ orbit} = \frac{2 \pi \left( 1.496\ 10^8 {\rm km} \right)}{3.16\ 10^7 {\rm seconds}}\)
 LHS diff is pdg0006081 - pdg0007427 RHS diff is 1.496 - 0.632911392405063*pdg0003141
12
  • 0000111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 6998364753
    \(v_{\rm Earth\ orbit} = \frac{2 \pi \left( 1.496\ 10^8 {\rm km} \right)}{3.16\ 10^7 {\rm seconds}}\)
  1. 4180845508
    \(v_{\rm Earth\ orbit} = 29.8 \frac{{\rm km}}{{\rm sec}}\)
 LHS diff is 0 RHS diff is 0.632911392405063*pdg0003141 - 29.8
13
  • 0000111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\ref{eq:#1} is one of the final equations.
  1. 4180845508
    \(v_{\rm Earth\ orbit} = 29.8 \frac{{\rm km}}{{\rm sec}}\)
no validation is available for declarations

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