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Review mass of the Earth

step inference rule input feed output step validity (as per SymPy)
0.5
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 5345738321
    \(F = m a\)
 no validation is available for declarations
1
  • 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. 5345738321
    \(F = m a\)
  1. 5781435087
    \(g\)
  2. 9881106100
    \(a\)
  1. 2484824786
    \(F = m g\)
 LHS diff is 0 RHS diff is pdg0005156*(-pdg0001649 + pdg0009140)
1.25
  • 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. 2484824786
    \(F = m g\)
  1. 2232825726
    \(g_{\rm Earth}\)
  2. 9355039511
    \(g\)
  1. 4800170179
    \(F = m g_{\rm Earth}\)
 LHS diff is 0 RHS diff is pdg0005156*(pdg0001649 - pdg0007557)
1.5
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 6935745841
    \(F = G \frac{m_1 m_2}{x^2}\)
 no validation is available for declarations
2
  • 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. 6935745841
    \(F = G \frac{m_1 m_2}{x^2}\)
  1. 6535639720
    \(r_{\rm Earth}\)
  2. 3353418803
    \(x\)
  3. 9903988330
    \(m\)
  4. 4651061153
    \(m_2\)
  5. 1193980495
    \(m_{\rm Earth}\)
  6. 3921072591
    \(m_1\)
  1. 8661803554
    \(F = G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}\)
 LHS diff is 0 RHS diff is pdg0004851*pdg0005022*pdg0006277/pdg0004037**2 - pdg0005156*pdg0005458*pdg0006277/pdg0003236**2
3
  • 0000111355: LHS of expr 1 equals LHS of expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • LHS of Eq.~\ref{eq:#1} is equal to LHS of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 4800170179
    \(F = m g_{\rm Earth}\)
  2. 8661803554
    \(F = G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2}\)
  1. 9407192813
    \(G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2} = m g_{\rm Earth}\)
 input diff is 0 diff is pdg0005156*pdg0007557 - pdg0005156*pdg0005458*pdg0006277/pdg0003236**2 diff is -pdg0005156*pdg0007557 + pdg0005156*pdg0005458*pdg0006277/pdg0003236**2
4
  • 0000111975: divide both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.
  1. 9407192813
    \(G \frac{m_{\rm Earth} m}{r_{\rm Earth}^2} = m g_{\rm Earth}\)
  1. 3246378279
    \(m\)
  1. 2308660627
    \(G \frac{m_{\rm Earth}}{r_{\rm Earth}^2} = g_{\rm Earth}\)
 valid
5
  • 0000111182: multiply both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Multiply both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.
  1. 2308660627
    \(G \frac{m_{\rm Earth}}{r_{\rm Earth}^2} = g_{\rm Earth}\)
  1. 2685587762
    \(\frac{r_{\rm Earth}^2}{G}\)
  1. 9440616166
    \(m_{\rm Earth} = \frac{g_{\rm Earth} r_{\rm Earth}^2}{G}\)
 valid
6
  • 0000111715: replace constant with value
  • number of inputs: 1; feeds: 3; outputs: 1
  • Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}
  1. 9440616166
    \(m_{\rm Earth} = \frac{g_{\rm Earth} r_{\rm Earth}^2}{G}\)
  1. 7816982139
    \(m/s^2\)
  2. 9590696981
    \(9.80665\)
  3. 2091584724
    \(g_{\rm Earth}\)
  1. 7846240076
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}\)
7
  • 0000111715: replace constant with value
  • number of inputs: 1; feeds: 3; outputs: 1
  • Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}
  1. 7846240076
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) r_{\rm Earth}^2}{G}\)
  1. 2957211007
    \(m^3 kg^{-1} s^{-2}\)
  2. 9956609318
    \(6.67430*10^{-11}\)
  3. 7326066466
    \(G\)
  1. 7112613117
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)
8
  • 0000111715: replace constant with value
  • number of inputs: 1; feeds: 3; outputs: 1
  • Replace constant $#1$ with value $#2$ and units $#3$ in Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}
  1. 7112613117
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) r_{\rm Earth}^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)
  1. 7560908617
    \(m\)
  2. 3723096423
    \(6.3781*10^6\)
  3. 7935917166
    \(r_{\rm Earth}\)
  1. 1132941271
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) (6.3781*10^6 m)^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)
9
  • 0000111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 1132941271
    \(m_{\rm Earth} = \frac{(9.80665 m/s^2) (6.3781*10^6 m)^2}{6.67430*10^{-11}m^3 kg^{-1} s^{-2}}\)
  1. 3364286646
    \(m_{\rm Earth} = 5.972*10^{24} kg\)
 LHS diff is 0 RHS diff is 6.3781 - 5.972e+24*kg

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