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
default for all languages	No label defined
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}}{2 G m + 2 G M}} (\sqrt{\frac{y}{y_{0}} (1 - \frac{y}{y_{0}})} + \arccos \sqrt{\frac{y}{y_{0}}})

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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 @@
- $t (y) = \sqrt{\frac{{y_{0}}^{3}}{2 G m M}} (\sqrt{\frac{y}{y_{0}} (1 - \frac{y}{y_{0}})} + \arccos \sqrt{\frac{y}{y_{0}}})$ 
t(y)= \sqrt{ \frac{ {y_0}^3 }{2GmM} } \left(\sqrt{\frac{y}{y_0}\left(1-\frac{y}{y_0}\right)} + \arccos{\sqrt{\frac{y}{y_0}}}  \right)
+ $t (y) = \sqrt{\frac{{y_{0}}^{3}}{2 G m + 2 G M}} (\sqrt{\frac{y}{y_{0}} (1 - \frac{y}{y_{0}})} + \arccos \sqrt{\frac{y}{y_{0}}})$ 
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

T4schmidt (talk | contribs)

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

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

$y$

$y_{0}$

$G$

$M$

$m$

Latest revision as of 20:10, 5 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

Free Fall Time (Q4496): Difference between revisions

T4schmidt (talk | contribs)

t(y)=y032GmM(yy0(1−yy0)+arccos⁡yy0)

t(y)=y032Gm+2GM(yy0(1−yy0)+arccos⁡yy0)

y

y0

G

M

m

Latest revision as of 20:10, 5 December 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

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

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

$y$

$y_{0}$

$G$

$M$

$m$