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--- 183_notes:newton_grav_pe [2018/05/29 21:38] – hallstein
+++ 183_notes:newton_grav_pe [2021/04/01 12:54] (current) – [Newtonian Gravitational Potential Energy] stumptyl
@@ Line 3: / Line 3: @@
 ===== Gravitational Potential Energy =====
-You have read about the [[183_notes:grav_pe|gravitational potential energy associated with a system consisting of an object and the Earth]]. This form of the gravitational potential energy turns about to be the [[183_notes:grav_pe_graphs#how_is_delta_u_mgh_an_approximation|approximate form of the potential energy]] for two objects that interact gravitationally. The gravitational potential energy is a powerful tool for modeling the motion of objects that interact through the gravitational force. It will help you to predict and explain the motion of large, massive objects such as planets, moons, and comets. In these notes, you will read about the general form of the gravitational potential energy.
+You have read about the [[183_notes:grav_pe|gravitational potential energy associated with a system consisting of an object and the Earth]]. This form of the gravitational potential energy turns about to be the [[183_notes:grav_pe_graphs#how_is_delta_u_mgh_an_approximation|approximate form of the potential energy]] for two objects that interact gravitationally. The gravitational potential energy is a powerful tool for modeling the motion of objects that interact through the gravitational force. It will help you to predict and explain the motion of large, massive objects such as planets, moons, and comets. **In these notes, you will read about the general form of the gravitational potential energy.**
 ==== Lecture Video ====
@@ Line 11: / Line 11: @@
 ==== (Near Earth) Gravitational Potential Energy ====
-Earlier, you read how the gravitational potential energy for a system consisting of two objects (the Earth and something on the surface of the Earth) is given by,
+Earlier, you read how the gravitational potential energy (J) for a system consisting of two objects (the Earth and something on the surface of the Earth) is given by,
  $\Delta U_{grav} = +mg\Delta y$
-where the separation distance ( $\Delta y$ ) is measured from the surface of the Earth. In this previous calculation, you assumed that the gravitational force was a constant ( $\vec{F}_{grav} = \langle 0,-mg,0\rangle$ ) over the distances that you were considering. This is an approximation, but it's not a bad one for the most part.
+where the separation distance ( $\Delta y$ ) is measured from the surface of the Earth. __In this previous calculation, you assumed that the gravitational force was a constant ( $\vec{F}_{grav} = \langle 0,-mg,0\rangle$ ) over the distances that you were considering.__ This is an approximation, but it's not a bad one for the most part.
 However, you will relax this condition now, because as you have read, that [[183_notes:gravitation|the gravitational force between two objects with mass is not a constant vector]].
-==== Newtonian Gravitational Potential Energy ====
+===== Newtonian Gravitational Potential Energy =====
 In general, the gravitational force exerted on a object of mass  $m_1$  due to an object of mass  $m_2$  is non-constant,
@@ Line 28: / Line 28: @@
 So for this force, what is the gravitational potential energy?
-=== Solve the 1-dimensional problem first ===
+==== Solve the One-Dimensional Problem First ====
 Remember that the potential energy change is the negative change in the internal work ( $\Delta U = -W_{int}$ ). So, you can calculate what the work done by the gravitational force would be and use that to determine that change in potential energy in going from location 1 to location 2,