Editing Tidal force (section)

== Size and distance ==
The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force.<ref name="Tyson"/> The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.<ref name="Sawicki1999"/>

[[File:Inverse x squaired.png|thumb|Figure 3: Graph showing how gravitational attraction drops off with increasing distance from a body]]
Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance ({{nowrap|1=''Y'' = 1/''X''<sup>2</sup>}}), while the slope ({{nowrap|1=''Y''{{′}} = −2/''X''<sup>3</sup>}}) is inversely proportional to the cube of the distance.

The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on the far side.  The tidal force becomes larger, when the two points are either farther apart, or when they are more to the left on the graph, meaning closer to the attracting body.

For example, even though the Sun has a stronger overall gravitational pull on Earth, the Moon creates a larger tidal bulge because the Moon is closer. This difference is due to the way gravity weakens with distance: the Moon's closer proximity creates a steeper decline in its gravitational pull as you move across Earth (compared to the Sun's very gradual decline from its vast distance). This steeper gradient in the Moon's pull results in a larger difference in force between the near and far sides of Earth, which is what creates the bigger tidal bulge.

Gravitational attraction is inversely proportional to the square of the distance from the source. The attraction will be stronger on the side of a body facing the source, and weaker on the side away from the source. The tidal force is proportional to the difference.<ref name="Sawicki1999">
{{cite journal
 |last1=Sawicki |first1=Mikolaj
 |title=Myths about gravity and tides
 |journal=[[The Physics Teacher]]
 |volume=37 |issue=7
 |year=1999
 |pages=438–441
 |issn=0031-921X |doi=10.1119/1.880345 |citeseerx=10.1.1.695.8981 |bibcode=1999PhTea..37..438S
}}</ref>

=== Sun, Earth, and Moon ===
The Earth is 81 times more massive than the Moon, the Earth has roughly 4 times the Moon's radius. As a result, at the same distance, the tidal force of the Earth at the surface of the Moon is about 20 times stronger than that of the Moon at the Earth's surface.<ref>
{{cite book
 |title=Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity
 |edition=illustrated
 |first1=Bernard |last1=Schutz
 |publisher=Cambridge University Press
 |year=2003
 |isbn=978-0-521-45506-0
 |page=45
 |url=https://books.google.com/books?id=P_T0xxhDcsIC
}} [https://books.google.com/books?id=P_T0xxhDcsIC&pg=PA45 Extract of page 45]</ref>

{| class="wikitable" 
! colspan="2"|Gravitational body causing tidal force !!colspan="3"| Body subjected to tidal force   !! Tidal acceleration
|-
! Body || Mass (<math>m</math>) || Body || Radius (<math>r</math>) || Distance (<math>d</math>) || <math> Gm ~ \frac{2r}{d^3} </math>
|-
| style="text-align: center" | '''Sun''' || style="text-align: center" | {{val|1.99|e=30|u=kg}} || '''Earth''' || style="text-align: center" | {{val|6.37|e=6|u=m}} || style="text-align: center" | {{val|1.50|e=11|u=m}} || style="text-align: center" | {{val|5.05|e=-7|u=m.s-2}}
|-
| style="text-align: center" | '''Moon''' || style="text-align: center" | {{val|7.34|e=22|u=kg}} || '''Earth''' || style="text-align: center" | {{val|6.37|e=6|u=m}} || style="text-align: center" | {{val|3.84|e=8|u=m}} || style="text-align: center" | {{val|1.10|e=-6|u=m.s-2}}
|-
| style="text-align: center" | '''Earth''' || style="text-align: center" | {{val|5.97|e=24|u=kg}} || '''Moon''' || style="text-align: center" | {{val|1.74|e=6|u=m}} || style="text-align: center" | {{val|3.84|e=8|u=m}} || style="text-align: center" | {{val|2.44|e=-5|u=m.s-2}}
|-
| colspan=6 style="background: #ffffff; font-size: small; font-weight: normal;" | ''G'' is the [[gravitational constant]] = {{physconst|G|round=3}}
|}