Physics 171: Chapter 12 - Newtons Law of Universal Gravitation and Kepler's Laws - Prof. W, Study notes of Physics

Information about various concepts in physics 171, such as newtons law of universal gravitation, potential energy, angular momentum conservation, and kepler's laws. It also includes formulas, examples, and problem-solving tips.

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Pre 2010

Uploaded on 02/13/2009

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Phys171 – Fri 4/5
Reminder HW 11 was due this morning
(please come see me after class if you forgot
and I will give an extension until Sun)
HW 12 DUE April 13
HW 13 DUE April 20 – THIS IS LONG
FINAL EXAM:
PHY 0405 Fri, May 18 8:00 am - 10:00 am
Newtons Law of Universal Gravitation
Force magnitude:
G Universal gravitational constant:
6.673 x 10-11 Nm2/ kg2
Note: For spherically symmetric objects, one can consider two
extended objects as point objects located at their center of
mass
Example: you on the earth surface. Can be modeled as two
point objects that are 6000km apart.
12
2
g
mm
FG
r
=
pf3
pf4

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Phys171 – Fri 4/

Reminder HW 11 was due this morning

(please come see me after class if you forgot

and I will give an extension until Sun)

HW 12 DUE April 13

HW 13 DUE April 20 – THIS IS LONG

FINAL EXAM:

PHY 0405 Fri, May 18 8:00 am - 10:00 am

Newtons Law of Universal Gravitation

Force magnitude:

G Universal gravitational constant :

6.673 x 10 -11^ N⋅m^2 / kg^2

Note: For spherically symmetric objects, one can consider two

extended objects as point objects located at their center of

mass

Example: you on the earth surface. Can be modeled as two

point objects that are 6000km apart.

g 2

m m

F G

r

  • This is an example of an inverse

square Force law

Potential Energy:

For earth’s gravity, r is measured relative to the center of the earth.

1 2 r

G

Gm m U r dU F dr

= −

=

Why do we get F=mg and U=mgh on the

earth surface?

Near the surface of the earth at height h:

Distance is still approximately earth radius:

r=RE +h

-> Approximate force and potential energy

2

2 9.8 2

= =

E

E

E

E

M m F G R

M m g G R s

2

=

E g

M m F G r

r distance to center of earth

Force balance: Kepler 3

rd

(Assume a circular orbit of radius r and period T )

Gravitational force = centripetal force

Note: K s is a constant -> T 2 proportional to r 3

2 Sun Planet Planet 2

GM M M v

r r

r

v

T

2 2 3

Sun 2 3

⎛ (^4) π ⎞ = ⎜ ⎟ ⎝ ⎠

= (^) S

T r GM

T K r

End chapter 12