Tidal tensor

In <a href="/facts/Newton%2527s_theory_of_gravitation/F6qH2XC3">Newton's theory of gravitation</a> and in various relativistic <a href="/facts/Classical_theories_of_gravitation/E51N6lSg">classical theories of gravitation</a>, such as <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>, the tidal tensor represents 

<ol><li>tidal accelerations of a cloud of (electrically neutral, nonspinning) <a href="/facts/Test_particle/EJfWtPRX">test particles</a>,</li>
<li>tidal stresses in a small object immersed in an ambient gravitational field.</li></ol>
The tidal tensor represents the relative acceleration due to gravity of two test masses separated by an <a href="/facts/Infinitesimal/JKcTMIgD">infinitesimal</a> distance. The component 
 
 
 
 
 Φ
 
 
 a
 
 
 b
 
 
 
 
 
 {\displaystyle \Phi _{{a}{b}}}
 
 represents the relative acceleration in the 
 
 
 
 
 
 
 a
 ^
 
 
 
 
 
 {\displaystyle {\hat {a}}}
 
 direction produced by a displacement in the 
 
 
 
 
 
 
 b
 ^
 
 
 
 
 
 {\displaystyle {\hat {b}}}
 
 direction.

Tidal tensor open-in-new

Tidal tensor