Important Reminders
 Last Lecture
Gravity far from the Surface
Intro to Gravity
 Exam #3 is next Friday at 10am.
 Today
More on Gravity
 Important Concepts
Gravity depends on the product of the two masses and
the inverse of the distance squared.
In the standard convention, the PE of gravity is negative.
 Force depends on:
 Current MasteringPhysics due tonight.
the product of the two masses
 Pset #9 due this Friday.
the inverse square of the distance
 IAP class schedule is posted under “General Info”.
 Next MasteringPhysics due next Monday.
11/29/2005
FG = !
8.01L Fall 2005
11/29/2005
Applications
! !
 Recall the general formula: PE(B) ! PE(A) = ! " Fids
A
Since only the difference matters, we pick some
point A and define PE(A)=0. For gravity, the
standard convention is to define A = !
Beware of the minus sign!
 Escape velocity
r
The minimum speed needed to get very far away from
some object
!
r
$ GM 1 M 2 '
r̂ ) idr̂
%
(
r2
"
 So: PE(r) = ! # Fidr̂ = ! # & !
"
 And the final result: PE(r) = !
8.01L Fall 2005
 Force: FG = !
B
Straightforward F=ma problem
11/29/2005
8.01L Fall 2005
11/29/2005
Gravity Summary
 A multitude of minus signs!
 Work & Energy
Nm 2
kg 2
GM 1 M 2
r̂
r2
8.01L Fall 2005
PE of Gravity
Circular orbits
G = 6.673 ! 10 "11
 Force points along the line between the two objects
in the direction to cause attraction
“Escape velocity” is the speed needed to get very far
away from something but with no speed left over.
8.01L Fall 2005
a universal constant:
GM 1 M 2
r̂
r2
 Energy: PE(r) = !
GM 1 M 2
r
 Escape velocity: ETotal = KE + PE = 0
GM 1 M 2
r
11/29/2005
8.01L Fall 2005
11/29/2005
1