Free Fall Time (Q4496): Difference between revisions

Latest revision as of 20:10, 5 December 2024

The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse.

Language	Label	Description	Also known as
English	Free Fall Time	The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse.

Statements

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https://en.wikipedia.org/wiki/Free-fall_time

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subclass of

time

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defining formula

t(y)={\sqrt {\frac {{y_{0}}^{3}}{2Gm+2GM}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)

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in defining formula

y

symbol represents

Free Fall Height

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y_{0}

symbol represents

Free Fall Initial Height

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G

symbol represents

Gravitational Constant

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M

symbol represents

Earth Mass

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m

symbol represents

Free Fall Mass

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Identifiers

Wikidata QID

Q5499609

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@@ Property / defining formula / Property / defining formula @@
- $t(y)={\sqrt {\frac {{y_{0}}^{3}}{2G}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$ 
t(y)= \sqrt{ \frac{ {y_0}^3 }{2G} } \left(\sqrt{\frac{y}{y_0}\left(1-\frac{y}{y_0}\right)} + \arccos{\sqrt{\frac{y}{y_0}}}  \right)
+ $t(y)={\sqrt {\frac {{y_{0}}^{3}}{2Gm+2GM}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$ 
t(y)= \sqrt{ \frac{ {y_0}^3 }{2Gm+2GM} } \left(\sqrt{\frac{y}{y_0}\left(1-\frac{y}{y_0}\right)} + \arccos{\sqrt{\frac{y}{y_0}}}  \right)
@@ Property / in defining formula @@
+ $y$ 
y
@@ Property / in defining formula: $y$ / rank @@
+Normal rank
@@ Property / in defining formula: $y$ / qualifier @@
+symbol represents: Free Fall Height
@@ Property / in defining formula @@
+ $y_{0}$ 
y_0
@@ Property / in defining formula: $y_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: $y_{0}$ / qualifier @@
+symbol represents: Free Fall Initial Height
@@ Property / in defining formula @@
+ $G$ 
G
@@ Property / in defining formula: $G$ / rank @@
+Normal rank
@@ Property / in defining formula: $G$ / qualifier @@
+symbol represents: Gravitational Constant
@@ Property / in defining formula @@
+ $M$ 
M
@@ Property / in defining formula: $M$ / rank @@
+Normal rank
@@ Property / in defining formula: $M$ / qualifier @@
+symbol represents: Earth Mass
@@ Property / in defining formula @@
+ $m$ 
m
@@ Property / in defining formula: $m$ / rank @@
+Normal rank
@@ Property / in defining formula: $m$ / qualifier @@
+symbol represents: Free Fall Mass

Free Fall Time (Q4496): Difference between revisions

$t(y)={\sqrt {\frac {{y_{0}}^{3}}{2G}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$

$t(y)={\sqrt {\frac {{y_{0}}^{3}}{2Gm+2GM}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$

$y$

$y_{0}$

$G$

$M$

$m$

Latest revision as of 20:10, 5 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

Free Fall Time (Q4496): Difference between revisions

t ( y ) = y 0 3 2 G ( y y 0 ( 1 − y y 0 ) + arccos ⁡ y y 0 ) {\displaystyle t(y)={\sqrt {\frac {{y_{0}}^{3}}{2G}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)}

t ( y ) = y 0 3 2 G m + 2 G M ( y y 0 ( 1 − y y 0 ) + arccos ⁡ y y 0 ) {\displaystyle t(y)={\sqrt {\frac {{y_{0}}^{3}}{2Gm+2GM}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)}

y {\displaystyle y}

y 0 {\displaystyle y_{0}}

G {\displaystyle G}

M {\displaystyle M}

m {\displaystyle m}

Latest revision as of 20:10, 5 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

$t(y)={\sqrt {\frac {{y_{0}}^{3}}{2G}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$

$t(y)={\sqrt {\frac {{y_{0}}^{3}}{2Gm+2GM}}}\left({\sqrt {{\frac {y}{y_{0}}}\left(1-{\frac {y}{y_{0}}}\right)}}+\arccos {\sqrt {\frac {y}{y_{0}}}}\right)$

$y$

$y_{0}$

$G$

$M$

$m$