This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
from \cite{1999_Tipler_Llewellyn}, page 9
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
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13 | declare final expr |
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no validation is available for declarations |
4180845508:
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4180845508:
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6 | substitute LHS of expr 1 into expr 2 |
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valid |
6348260313:
3046191961: 3080027960: |
6348260313:
3046191961: 3080027960: |
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12 | simplify |
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LHS diff is 0 RHS diff is 0.632911392405063*pi - 29.8 |
6998364753:
error for dim with 6998364753 4180845508: |
6998364753:
N/A 4180845508: |
|
9 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is pdg6081*(0.666666666666667*pdg3141 - 0.632911392405063*pi) |
8721295221:
3080027960: 4593428198: error for dim with 4593428198 |
8721295221:
3080027960: 4593428198: N/A |
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3 | declare initial expr |
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no validation is available for declarations |
6785303857:
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6785303857:
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circumference of a circle |
10 | declare assumption |
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no validation is available for declarations |
3472836147:
error for dim with 3472836147 |
3472836147:
N/A |
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2 | change variable X to Y |
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valid |
5426308937:
6946088325: |
5426308937:
6946088325: |
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7 | declare assumption |
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no validation is available for declarations |
7175416299:
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7175416299:
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5 | change three variables in expr |
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valid |
6946088325:
3046191961: |
6946088325:
3046191961: |
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4 | change two variables in expr |
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valid |
6785303857:
6348260313: |
6785303857:
6348260313: |
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8 | multiply RHS by unity |
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feed diff is 364 LHS diff is 0 RHS diff is 362 |
7175416299:
8721295221: |
7175416299:
8721295221: |
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1 | declare initial expr |
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no validation is available for declarations |
5426308937:
|
5426308937:
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11 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is 0.313924050632911*pi |
3472836147:
error for dim with 3472836147 4593428198: error for dim with 4593428198 6998364753: error for dim with 6998364753 |
3472836147:
N/A 4593428198: N/A 6998364753: N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
---|---|---|---|---|---|---|---|---|---|
6081 | constant |
r_{\rm Earth\ orbit}
\(r_{\rm Earth\ orbit}\) |
['real'] |
|
radius of Earth's orbit |
1.496*10^8 km |
5 | ||
1467 | variable |
t
\(t\) |
['real'] |
|
time |
|
120 | ||
3141 | constant |
\pi
\(\pi\) |
['real'] | dimensionless | pi |
3.1415 dimensionless |
55 | ||
2530 | variable |
r
\(r\) |
['real'] |
|
radius | 34 | |||
1357 | variable |
v
\(v\) |
['real'] |
|
velocity |
|
80 | ||
7427 | variable |
v_{\rm Earth\ orbit}
\(v_{\rm Earth\ orbit}\) |
real |
|
velocity of Earth's orbit around sun |
|
6 | ||
1534 | variable |
C_{\rm Earth\ orbit}
\(C_{\rm Earth\ orbit}\) |
real |
|
circumference of Earth's orbit | 4 | |||
3034 | variable |
C
\(C\) |
['real'] |
|
circumference | 5 | |||
5344 | variable |
t_{\rm Earth\ orbit}
\(t_{\rm Earth\ orbit}\) |
real |
|
time of Earth's orbit around sun |
|
5 | ||
1943 | variable |
d
\(d\) |
['real'] |
|
displacement | 25 |