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--- 183_notes:gravitation [2021/02/04 23:49] – [The Gravitational Force] stumptyl
+++ 183_notes:gravitation [2021/02/05 00:01] (current) – [Newton's 3rd Law] stumptyl
@@ Line 46: / Line 46: @@
 The gravitational force provides the first example of [[http://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton.27s_third_law|Newton's 3rd Law]], which you might have heard colloquially as "For every action, there is an equal and opposite reaction." Unfortunately, [[http://www.wired.com/2013/10/a-closer-look-at-newtons-third-law/|this colloquialism is a terribly inaccurate definition]] that gets applied incorrectly quite often, [[http://scienceblogs.com/dotphysics/2010/05/06/mythbusters-energy-explanation/|even by the Mythbusters]]!
-Newton's 3rd Law results from the idea that a [[:183_notes:momentum_principle#net_force|force quantifies the interaction between two objects]]. You can also think of it as an empirical fact, which stems from our definition of force. That is, we observe when one object exerts a force on another object, the second object exerts a force on the first object of the same size but opposite in direction.
+Newton's 3rd Law results from the idea that a [[:183_notes:momentum_principle#net_force|force quantifies the interaction between two objects]]. You can also think of it as an empirical fact, which stems from our definition of force. That is, **we observe when one object exerts a force on another object, the second object exerts a force on the first object of the same size but opposite in direction.**
 To be more concrete, you can think about the gravitational interaction between the Earth and the moon (shown in the figure below). The magnitude of these gravitational forces are the same (see the equation above), but the vector direction for each always points directly towards the other object.
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 We will find other examples of Newton's 3rd Law pairs when you learn about [[183_notes:friction|contact interactions]]. When we discuss contact interactions, it turns out, these are the result of the electrostatic force.
+\\
 === If the forces are the same size, why isn't the motion the same? ===
 The motion of systems is governed by the [[183_notes:momentum_principle|Momentum Principle]]. In this case, you might find it useful to think about the [[183_notes:acceleration|acceleration of the system]], which tells you how the velocity of the system changes. While the Earth and Moon experience the same size gravitational force, the small mass of the Moon (compared to the Earth) results in a much larger acceleration for the Moon, and this change in the Moon's velocity is large (compared to the Earth's).
+\\
 === Acceleration due to the gravitational force ===
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 $$|a_{Earth}| = \dfrac{|F_{grav}|}{M_{Earth}} = G\dfrac{m_{person}}{R_{Earth}^2}$$
-Thus, the acceleration that the Earth would experience due a single person is about 0.0000000000000000000001*$g$! This value is incredibly small; we often neglect changes in the motion of the Earth due to objects that are not astronomically large. In these notes, the [[183_notes:grav_accel|vector acceleration due to gravitational interactions is calculated explicitly]].
+Thus, the acceleration that the Earth would experience due a single person is about 0.0000000000000000000001*$g$! This value is __incredibly small__; we often neglect changes in the motion of the Earth due to objects that are not astronomically large. In these notes, the [[183_notes:grav_accel|vector acceleration due to gravitational interactions is calculated explicitly]].
 ==== (More) Modern Gravitational Models ====
-Newton's model of the gravitational force was considered one of the simplest and most explanatory models for many years. We have since made observations that no longer fit with Newton's model (e.g., [[http://en.wikipedia.org/wiki/Gravitational_lens|Gravitational lensing]]). Our best model for gravitation, which observations continue to fit, is called [[http://en.wikipedia.org/wiki/General_relativity|"general relativity"]] (GR) and was developed by [[http://en.wikipedia.org/wiki/Albert_Einstein|Albert Einstein]]. While this model provides us with far better predictions and explanations of a variety of observations, we still use Newton's model of the gravitational force for two reasons: (1) it can provide reasonable predictions for many cases, and (2) [[https://en.wikipedia.org/wiki/Mathematics_of_general_relativity|the mathematics that is used in GR]] is sufficiently sophisticated that you will need more physics and mathematics experience to gain deep insight into its use.
+Newton's model of the gravitational force was considered one of the simplest and most explanatory models for many years. We have since made observations that no longer fit with Newton's model (e.g., [[http://en.wikipedia.org/wiki/Gravitational_lens|Gravitational lensing]]). Our best model for gravitation, which observations continue to fit, is called [[http://en.wikipedia.org/wiki/General_relativity|"general relativity"]] (GR) and was developed by [[http://en.wikipedia.org/wiki/Albert_Einstein|Albert Einstein]]. While this model provides us with far better predictions and explanations of a variety of observations, we still use Newton's model of the gravitational force for two reasons: (1) //it can provide reasonable predictions for many cases//, and (2) //[[https://en.wikipedia.org/wiki/Mathematics_of_general_relativity|the mathematics that is used in GR]] is sufficiently sophisticated that you will need more physics and mathematics experience to gain deep insight into its use.
+//
 ===== Examples =====
   * [[183_notes:examples:calcGravForce|Calculating the Gravitational Force]]
   * [[183_notes:examples:videoswk3|Video Example: Gravitational force and Kinematic equations on the Moon]]