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Review Newton's Law of Gravitation

abstract: from https://www.youtube.com/watch?v=fJYdFIZlD8k
reference:

step	inference rule	input	feed	output	validity (as per SymPy)
17	ID: 111732; substitute LHS of two expressions into expression number of inputs: 3; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} and LHS of Eq.~\\ref{eq:#2} into Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.				recognized infrule but not yet supported
8	ID: 111556; 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}.	4820320578 $F_{gravitational}=F_{centripetal}$ 6026694087 $F_{centripetal}=m \frac{v^2}{r}$		4267808354 $F_{gravitational}=m \frac{v^2}{r}$	LHS diff is pdg0001687 - pdg0002867 RHS diff is pdg0005156(-pdg00013572 + v*2)/pdg0002530
10	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			6785303857 $C=2 \pi r$	no validation is available for declarations
9	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			3411994811 $v_{\rm average}=\frac{d}{t}$	no validation is available for declarations
5	ID: 111104; declare assumption number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an assumption.			4820320578 $F_{gravitational}=F_{centripetal}$	no validation is available for declarations
19	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	1292735067 $F_{gravitational}=G \frac{m_1 m_2}{r^2}$			no validation is available for declarations
7	ID: 111556; 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}.	5345738321 $F=m a$ 8361238989 $a_{centripetal}=\frac{v^2}{r}$		6026694087 $F_{centripetal}=m \frac{v^2}{r}$	LHS diff is a_{c(e(n(t(r(i(p(e(t(al)))))))))} - pdg0001687 RHS diff is (pdg0001357*2 - pdg0005156v**2)/pdg0002530
15	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	3004158505 $\frac{T^2}{r} F_{gravitational}=\left( \frac{4 \pi^2 m r}{T^2} \right)\frac{T^2}{r}$		3650370389 $\frac{T^2}{r} F_{gravitational}=4 \pi^2 m$	valid
11	ID: 111556; 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}.	6785303857 $C=2 \pi r$ 3411994811 $v_{\rm average}=\frac{d}{t}$		5177311762 $v=\frac{2 \pi r}{T}$	LHS diff is -pdg0001357 + pdg0006709 RHS diff is -2pdg0002530pdg0003141/pdg0008762 + pdg0001943/pdg0001467
3	ID: 111886; 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}.		3876446703 $m$ 7905984866 $m_1$		list index out of range
18	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.			1292735067 $F_{gravitational}=G \frac{m_1 m_2}{r^2}$	list index out of range
13	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	6268336290 $F_{gravitational}=\frac{m}{r}\left(\frac{2\pi r}{T}\right)^2$		7672365885 $F_{gravitational}=\frac{4 \pi^2 m r}{T^2}$	valid
14	ID: 111182; 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}.	7672365885 $F_{gravitational}=\frac{4 \pi^2 m r}{T^2}$	3448601530 $\frac{T^2}{r}$	3004158505 $\frac{T^2}{r} F_{gravitational}=\left( \frac{4 \pi^2 m r}{T^2} \right)\frac{T^2}{r}$	LHS arithmetic error. Diff: pdg0002867(-pdg00087622 + pdg0009491*2)/pdg0002530
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5345738321 $F=m a$	no validation is available for declarations
6	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			8361238989 $a_{centripetal}=\frac{v^2}{r}$	no validation is available for declarations
4	ID: 111886; 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}.		9594072504 $m_2$ 2346952973 $m$		list index out of range
12	ID: 111556; 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}.	4267808354 $F_{gravitational}=m \frac{v^2}{r}$ 5177311762 $v=\frac{2 \pi r}{T}$		6268336290 $F_{gravitational}=\frac{m}{r}\left(\frac{2\pi r}{T}\right)^2$	LHS diff is pdg0001357 - pdg0002867 RHS diff is 2pdg0002530pdg0003141(-2pdg0003141pdg0004851 + pdg0008762)/pdg0008762*2
16	ID: 111237; declare guess solution number of inputs: 1; feeds: 0; outputs: 1 Judicious choice as a guessed solution to Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2},	3650370389 $\frac{T^2}{r} F_{gravitational}=4 \pi^2 m$			no validation is available for declarations
2	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	5345738321 $F=m a$			list index out of range

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timing of Neo4j queries:

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