Gravitational Force Near Earth - Revision history

DylanJMount at 04:05, 3 December 2025

2025-12-03T04:05:18Z

@@ Line 68: / Line 68: @@
 ::ball.pos = ball.pos + ball.vel * deltat
 </code>
 ==Examples==

DylanJMount at 03:59, 3 December 2025

2025-12-03T03:59:09Z

← Older revision		Revision as of 23:59, 2 December 2025
Line 1:		Line 1:
	'''[~~Nahli Jinks Fall 2022~~]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.		'''[[Dylan Mount – Spring 2025]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.
	~~CLAIMED BY: NIA THOMPSON SPR 25~~

	==Main Idea==		==Main Idea==
	~~Near~~ Earth~~'s surface~~, the ~~magnitude of~~ acceleration ~~due~~ gravity ~~is approximately constant~~. ~~Newton's~~ Law of Universal Gravitation ~~states~~ that ~~any two bodies attract~~ each other ~~with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects~~. ~~If we approximate the Earth as a point mass, we find that the distance to the surface is simply the radius~~ of ~~the Earth. We now want to apply Newton's Law of Universal Gravitation to our approximation and see if we can calculate the acceleration due to gravity near Earth's surface. Generally~~ this ~~is only acceptable because~~ the ~~distance between the object of interest~~ and ~~Earth's surface is <math> << </math> the distance~~ from ~~the center of the Earth to Earth's surface. Thus the difference in distances is so small that the result is well-approximated using only Earth's radius~~.		Close to the surface of the Earth, the acceleration caused by gravity remains roughly the same. Newton’s Law of Universal Gravitation tells us that every pair of masses pulls on each other. The strength of this attraction depends on how big the masses are and how far apart they are from each other.

			When we think of Earth as a point mass, we can say that an object sitting on the surface is about one Earth radius away from the center of our planet. The height of most everyday objects is so tiny compared to the vast radius of the Earth that the difference in distance is practically unnoticeable. This explains why we can consider gravitational acceleration g to be constant near the surface of the Earth.

	===A Mathematical Model===		===A Mathematical Model===
Line 34:		Line 34:
	===The Gravitational Field===		===The Gravitational Field===
	[[File:Newtons2LawImage344.png\|thumb\|left\|Distance between the centers of mass of Earth and an object on its surface to be the radius of Earth.]]		[[File:Newtons2LawImage344.png\|thumb\|left\|Distance between the centers of mass of Earth and an object on its surface to be the radius of Earth.]]
	The gravitational field ~~describes~~ the ~~area~~ that ~~is created by a mass~~. The ~~field exerts a force on the objects inside the field depending on the magnitude~~ of the field ~~and~~ the mass ~~of the object inside the field~~. ~~The~~ lines in the ~~image below represent the field lines. The magnitude of the field is inversely proportional the the spacing of the lines. The direction~~ of ~~vector ''g'' will always be parallel to~~ the ~~field lines, which will always be equally spaced and distributed. Objects inside of~~ Earth~~'s gravitational field, feel the force called ''weight''~~ and in the ~~case~~ of ~~Earth's gravitational~~ field~~, the center of gravity is equal to its center of mass. As a result, we have the gravitational constant ''g''~~.		The gravitational field shows us how a mass affects the space that surrounds it. The strength of the field at a specific point influences the gravitational force that a mass feels when it is positioned there.

			Field lines move toward the center of the Earth and become more concentrated as the strength of the field increases.
	[[File:Gravitational field Earth lines equipotentials.svg\|thumb\|Gravitational field lines]]		[[File:Gravitational field Earth lines equipotentials.svg\|thumb\|Gravitational field lines]]

	~~To get the force of gravity~~ in vector form~~, we can use the equation below.~~
			The gravitational field strength can be expressed in vector form as:

	:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>		:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>

Line 43:		Line 47:
	::Your weight is ''not'' the same, however the significance that it changes is negligible if you are just traveling to the top of a building. Although you are further from the Earth's center of mass, the difference in distance from the Earth's center of mass is too small to significantly change your weight. Although your weight may change in varying levels due to your distance from Earth's surface, your mass will always stay the same. This is because <math> {F} = {ma} </math>		::Your weight is ''not'' the same, however the significance that it changes is negligible if you are just traveling to the top of a building. Although you are further from the Earth's center of mass, the difference in distance from the Earth's center of mass is too small to significantly change your weight. Although your weight may change in varying levels due to your distance from Earth's surface, your mass will always stay the same. This is because <math> {F} = {ma} </math>

			===Common Misunderstandings About Gravity===
			Some common beliefs about gravity might not be as accurate as we think. Addressing these misunderstandings fosters a deeper understanding of physics and helps prevent typical errors during exams.


			'''1. "Heavier objects tend to fall faster than those that are lighter."'''
			This isn't true when air resistance is not a factor. Close to the surface of our planet, everything falls at the same speed, with an acceleration of <math> g = 9.8 \frac{m}{s^2} </math>, no matter how heavy or light it is. Although heavier objects feel a stronger gravitational ''force'' (as described by <math> F = mg </math>), they do ''not'' undergo a greater acceleration.

			'''2. "Astronauts in orbit feel weightless."'''
			Astronauts remain firmly within the embrace of Earth's gravitational pull. They float because they are constantly falling towards Earth, which gives us that feeling of weightlessness. At typical orbital altitudes, gravity remains roughly 90% of what we experience on the surface.

			'''3. " No matter where you are on Earth, your weight remains constant."'''
			The weight of an object is influenced by how far it is from the center of the Earth and the way mass is distributed within the Earth itself. Your weight is a bit lighter at the equator due to the Earth's larger radius in that region, while you feel a bit heavier at the poles. The variations may be slight, yet they can be quantified.

	===A Computational Model===		===A Computational Model===

Nthompson74 at 03:38, 14 April 2025

2025-04-14T03:38:15Z

← Older revision		Revision as of 23:38, 13 April 2025
Line 1:		Line 1:
	'''[Nahli Jinks Fall 2022]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.		'''[Nahli Jinks Fall 2022]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.
			CLAIMED BY: NIA THOMPSON SPR 25

	==Main Idea==		==Main Idea==

Njinks3 at 23:58, 4 December 2022

2022-12-04T23:58:26Z

← Older revision		Revision as of 19:58, 4 December 2022
Line 16:		Line 16:

	Since the only forces acting on a object in free fall near earth's surface are it's weight, (mass and gravity), we can set <math> {F}_{grav} = {mg} </math> ,and then plug that into Newton's Law of Universal Gravitation. After canceling out the constants, we arrive at the gravitational constant for a free falling object near earth.		Since the only forces acting on a object in free fall near earth's surface are it's weight, (mass and gravity), we can set <math> {F}_{grav} = {mg} </math> ,and then plug that into Newton's Law of Universal Gravitation. After canceling out the constants, we arrive at the gravitational constant for a free falling object near earth.
			::<math> {g} = \frac{GM_{Earth}}{R_{Earth}^2}</math>

	::<math> ~~{g} =~~ \frac{~~GM_{Earth}~~}{~~R_{Earth}~~^2}</math>		Near Earth's surface ''g'' is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:
	~~[[File~~:~~Newtons2LawImage344.png\|thumb\|Distance between the centers of mass of Earth and an object on its surface to be the radius of Earth.]]~~

	Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:
	::<math>C= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>		::<math>C= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>


	This then puts the force near Earth due to gravity into a much simpler form:		This then puts the force near Earth due to gravity into a much simpler form:
Line 29:		Line 29:
	::* ''m'' is the mass of the object whose behavior we are interested in		::* ''m'' is the mass of the object whose behavior we are interested in

	The gravitation constant ''g'' applies to all masses significantly smaller than Earth's mass. These masses will all fall at the same acceleration.		The gravitation constant ''g'' applies to all masses ''significantly'' smaller than Earth's mass. These masses will all fall at the same acceleration.

	===The Gravitational Field===		===The Gravitational Field===
	To get the force of gravity in vector form, we can use ~~this~~ equation:		[[File:Newtons2LawImage344.png\|thumb\|left\|Distance between the centers of mass of Earth and an object on its surface to be the radius of Earth.]]
			The gravitational field describes the area that is created by a mass. The field exerts a force on the objects inside the field depending on the magnitude of the field and the mass of the object inside the field. The lines in the image below represent the field lines. The magnitude of the field is inversely proportional the the spacing of the lines. The direction of vector ''g'' will always be parallel to the field lines, which will always be equally spaced and distributed. Objects inside of Earth's gravitational field, feel the force called ''weight'' and in the case of Earth's gravitational field, the center of gravity is equal to its center of mass. As a result, we have the gravitational constant ''g''.
			[[File:Gravitational field Earth lines equipotentials.svg\|thumb\|Gravitational field lines]]

			To get the force of gravity in vector form, we can use the equation below.
	:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>		:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>
	~~[[File:Gravitational field Earth lines equipotentials.svg\|Gravitational_field_Earth_lines_equipotentials]]~~

			'''Conceptual Question''': Say you are standing in the basement of a building and weigh yourself. Then you immediately go to the 10th floor of the same building and weigh yourself again. Is your weight the same?
			::Your weight is ''not'' the same, however the significance that it changes is negligible if you are just traveling to the top of a building. Although you are further from the Earth's center of mass, the difference in distance from the Earth's center of mass is too small to significantly change your weight. Although your weight may change in varying levels due to your distance from Earth's surface, your mass will always stay the same. This is because <math> {F} = {ma} </math>


	===A Computational Model===		===A Computational Model===
	Using the approximation derived above, we can create a computational model for the force of gravity near Earth's surface by applying Newton's second law in an iterative fashion to update acceleration, velocity, and finally position. This allows us to simulate the motion of an object near Earth's surface using only its mass. Seen below is a GlowScript code snippet accomplishing this iterative update technique.		Using the approximation derived above, we can create a computational model for the force of gravity near Earth's surface by applying Newton's second law in an iterative fashion to update acceleration, velocity, and finally position. This allows us to simulate the motion of an object near Earth's surface using only its mass. Seen below is a GlowScript code snippet accomplishing this iterative update technique.
Line 79:		Line 86:

	==History==		==History==
	Prior to the age of Newton, gravity as a force was a totally foreign concept. During the 17th century, Galileo realized that all objects, regardless of mass, fall with the same acceleration towards Earth. It was in 1687 when Newton published his ''Principia'' that he hypothesized that gravity acts as a force whose magnitude is inversely proportional to the square of distance between objects. This description was incomplete, however, and remained unfinished until Cavendish determined the value of ''G'', the universal gravitational constant.		Prior to the age of Newton, gravity as a force was a totally foreign concept. During the 17th century, Galileo realized that all objects, regardless of mass, fall with the same acceleration towards Earth. It was in 1687 when Newton published his ''Principia'' that he hypothesized that gravity acts as a force whose magnitude is inversely proportional to the square of distance between objects. This description was incomplete, however, and remained unfinished until Cavendish determined the value of ''G'', the universal gravitational constant. The purpose of this venture was to eventually determine the mass of Earth, which one he found the value of ''G'', he could determine.

	==Connectedness==		==Connectedness==

	1.How is this topic connected to something that you are interested in?		1.How is this topic connected to something that you are interested in?
	::		:: I am personally interested in our solar system, and how the planets have orbited each other. The gravitational fields of each planet and their moons control how how solar system orbits.

	2. How is it connected to your major?		2. How is it connected to your major?
	::As a civil engineering major, in general understanding the laws of physics ensures that the tools and construction we create are safe and realistic. ~~Understanding~~ the		::As a civil engineering major, in general understanding the laws of physics ensures that the tools and construction we create are safe and realistic. Research on gravitational fields has allowed civil engineers to test the bounds of construction, and also know when gravitational fields need not be considered.
	Is there an interesting industrial application?
			3. Is there an interesting industrial application?
			The leaning tower of Pisa is an example of civil and structural engineers using gravitational fields to their advantage. They calculated the center of mass of the tower, and the center of mass is not outside of the base, allowing it to tilt without ever falling.

	==See Also==		==See Also==

Njinks3 at 22:47, 4 December 2022

2022-12-04T22:47:13Z

← Older revision		Revision as of 18:47, 4 December 2022
Line 18:		Line 18:

	::<math> {g} = \frac{GM_{Earth}}{R_{Earth}^2}</math>		::<math> {g} = \frac{GM_{Earth}}{R_{Earth}^2}</math>
			[[File:Newtons2LawImage344.png\|thumb\|Distance between the centers of mass of Earth and an object on its surface to be the radius of Earth.]]

	Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:		Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:
	::C= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>		::<math>C= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>

	This then puts the force near Earth due to gravity into a much simpler form:		This then puts the force near Earth due to gravity into a much simpler form:
Line 34:		Line 34:
	To get the force of gravity in vector form, we can use this equation:		To get the force of gravity in vector form, we can use this equation:
	:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>		:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>
	[[File:Gravitational field.~~png~~\|~~Gravitational field~~]]		[[File:Gravitational field Earth lines equipotentials.svg\|Gravitational_field_Earth_lines_equipotentials]]

	===A Computational Model===		===A Computational Model===

Njinks3 at 22:33, 4 December 2022

2022-12-04T22:33:33Z

← Older revision		Revision as of 18:33, 4 December 2022
Line 3:		Line 3:
	==Main Idea==		==Main Idea==
	Near Earth's surface, the magnitude of acceleration due gravity is approximately constant. Newton's Law of Universal Gravitation states that any two bodies attract each other with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects. If we approximate the Earth as a point mass, we find that the distance to the surface is simply the radius of the Earth. We now want to apply Newton's Law of Universal Gravitation to our approximation and see if we can calculate the acceleration due to gravity near Earth's surface. Generally this is only acceptable because the distance between the object of interest and Earth's surface is <math> << </math> the distance from the center of the Earth to Earth's surface. Thus the difference in distances is so small that the result is well-approximated using only Earth's radius.		Near Earth's surface, the magnitude of acceleration due gravity is approximately constant. Newton's Law of Universal Gravitation states that any two bodies attract each other with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects. If we approximate the Earth as a point mass, we find that the distance to the surface is simply the radius of the Earth. We now want to apply Newton's Law of Universal Gravitation to our approximation and see if we can calculate the acceleration due to gravity near Earth's surface. Generally this is only acceptable because the distance between the object of interest and Earth's surface is <math> << </math> the distance from the center of the Earth to Earth's surface. Thus the difference in distances is so small that the result is well-approximated using only Earth's radius.






Line 25:		Line 21:

	Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:		Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:
	::~~<math> g = \frac{GM_{Earth}}{R_{Earth}^2}~~= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>		::C= \frac{(6.6710^{-11} \frac{m^3}{kgs})(5.97210^{24} kg)}{(6.378*10^{6} m)^2} = 9.8 \frac{m}{s^2}</math>

	This then puts the force near Earth due to gravity into a much simpler form:		This then puts the force near Earth due to gravity into a much simpler form:
Line 36:		Line 32:

	===The Gravitational Field===		===The Gravitational Field===
			To get the force of gravity in vector form, we can use this equation:
			:: <math> \vec g = \frac{GM}{r^2} \hat r\ </math>
			[[File:Gravitational field.png\|Gravitational field]]

	===A Computational Model===		===A Computational Model===
Line 81:		Line 80:
	==History==		==History==
	Prior to the age of Newton, gravity as a force was a totally foreign concept. During the 17th century, Galileo realized that all objects, regardless of mass, fall with the same acceleration towards Earth. It was in 1687 when Newton published his ''Principia'' that he hypothesized that gravity acts as a force whose magnitude is inversely proportional to the square of distance between objects. This description was incomplete, however, and remained unfinished until Cavendish determined the value of ''G'', the universal gravitational constant.		Prior to the age of Newton, gravity as a force was a totally foreign concept. During the 17th century, Galileo realized that all objects, regardless of mass, fall with the same acceleration towards Earth. It was in 1687 when Newton published his ''Principia'' that he hypothesized that gravity acts as a force whose magnitude is inversely proportional to the square of distance between objects. This description was incomplete, however, and remained unfinished until Cavendish determined the value of ''G'', the universal gravitational constant.

			==Connectedness==

			1.How is this topic connected to something that you are interested in?
			::
			2. How is it connected to your major?
			::As a civil engineering major, in general understanding the laws of physics ensures that the tools and construction we create are safe and realistic. Understanding the
			Is there an interesting industrial application?

	==See Also==		==See Also==

Njinks3 at 21:31, 4 December 2022

2022-12-04T21:31:20Z

← Older revision		Revision as of 17:31, 4 December 2022
Line 3:		Line 3:
	==Main Idea==		==Main Idea==
	Near Earth's surface, the magnitude of acceleration due gravity is approximately constant. Newton's Law of Universal Gravitation states that any two bodies attract each other with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects. If we approximate the Earth as a point mass, we find that the distance to the surface is simply the radius of the Earth. We now want to apply Newton's Law of Universal Gravitation to our approximation and see if we can calculate the acceleration due to gravity near Earth's surface. Generally this is only acceptable because the distance between the object of interest and Earth's surface is <math> << </math> the distance from the center of the Earth to Earth's surface. Thus the difference in distances is so small that the result is well-approximated using only Earth's radius.		Near Earth's surface, the magnitude of acceleration due gravity is approximately constant. Newton's Law of Universal Gravitation states that any two bodies attract each other with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects. If we approximate the Earth as a point mass, we find that the distance to the surface is simply the radius of the Earth. We now want to apply Newton's Law of Universal Gravitation to our approximation and see if we can calculate the acceleration due to gravity near Earth's surface. Generally this is only acceptable because the distance between the object of interest and Earth's surface is <math> << </math> the distance from the center of the Earth to Earth's surface. Thus the difference in distances is so small that the result is well-approximated using only Earth's radius.






	===A Mathematical Model===		===A Mathematical Model===
	From Newton's Law of Universal Gravitation we know:		From Newton's Law of Universal Gravitation we know:
	::<math> {F}_{grav}=G \frac{m_1 m_2}{r^2}\ </math>		::<math> {F}_{grav}=G \frac{m_1 m_2}{r^2}\ </math>
			Where
	~~:where,~~
	::* ''F'' is the gravitational force between the masses;		::* ''F'' is the gravitational force between the masses;
	::* ''G'' is the [https://en.wikipedia.org/wiki/Gravitational_constant gravitational constant], <math>6.674×10^{−11} \frac{N m^2}{kg^2}\ </math>;		::* ''G'' is the [https://en.wikipedia.org/wiki/Gravitational_constant gravitational constant], <math>6.674×10^{−11} \frac{N m^2}{kg^2}\ </math>;
Line 14:		Line 18:
	::* ''m''<sub>2</sub> is the mass of the second object;		::* ''m''<sub>2</sub> is the mass of the second object;
	::* ''r'' is the distance between the objects.		::* ''r'' is the distance between the objects.

			Since the only forces acting on a object in free fall near earth's surface are it's weight, (mass and gravity), we can set <math> {F}_{grav} = {mg} </math> ,and then plug that into Newton's Law of Universal Gravitation. After canceling out the constants, we arrive at the gravitational constant for a free falling object near earth.

			::<math> {g} = \frac{GM_{Earth}}{R_{Earth}^2}</math>


	Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:		Near Earth's surface, however, <math> \frac{GM_{Earth}}{R_{Earth}^2}</math> is unchanging. As such, we define it as the gravitational constant near Earth's surface, ''g'', which is approximately <math>9.8 \frac{m}{s^2} </math>. This calculation is shown below:
Line 20:		Line 29:
	This then puts the force near Earth due to gravity into a much simpler form:		This then puts the force near Earth due to gravity into a much simpler form:
	:: <math>\|\vec{\mathbf{F}}_{grav}\|= mg </math>		:: <math>\|\vec{\mathbf{F}}_{grav}\|= mg </math>
			Where
	~~:where,~~
	::* ''g'' is the near-Earth gravitational constant, as defined above to be <math>9.8 \frac{m}{s^2} </math>		::* ''g'' is the near-Earth gravitational constant, as defined above to be <math>9.8 \frac{m}{s^2} </math>
	::* ''m'' is the mass of the object whose behavior we are interested in		::* ''m'' is the mass of the object whose behavior we are interested in

			The gravitation constant ''g'' applies to all masses significantly smaller than Earth's mass. These masses will all fall at the same acceleration.

			===The Gravitational Field===

	===A Computational Model===		===A Computational Model===

Njinks3 at 20:31, 4 December 2022

2022-12-04T20:31:25Z

← Older revision		Revision as of 16:31, 4 December 2022
Line 1:		Line 1:
	'''[~~William Beard~~ Fall ~~2021~~]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.		'''[Nahli Jinks Fall 2022]''' This section describes gravitational force near Earth's surface, including applications and relevant derivations.

	==Main Idea==		==Main Idea==

Wbeard8 at 03:40, 6 December 2021

2021-12-06T03:40:59Z

Show changes

Lduffy8: /* A Computational Model */

2019-06-27T02:18:57Z

A Computational Model

← Older revision		Revision as of 22:18, 26 June 2019
Line 24:		Line 24:
	::* ''g'' is the near-Earth gravitational constant, as defined above to be <math>9.8 \frac{m}{s^2} </math>		::* ''g'' is the near-Earth gravitational constant, as defined above to be <math>9.8 \frac{m}{s^2} </math>
	::* ''m'' is the mass of the object whose behavior we are interested in		::* ''m'' is the mass of the object whose behavior we are interested in

	~~===A Computational Model===~~

	==Examples==		==Examples==