Transcript Keppler`s laws

PH 201
Dr. Cecilia Vogel
Lecture 23
REVIEW
equilibrium
stable vs. unstable
static
OUTLINE
eqlb
universal gravitation
Universal Gravity
Newton’s Universal Law of Gravity:
Gm1m2
U 
r
Gm1m2
F 
2
r
applies universally
Applies to surface of planet
Applies to orbiting satellites
Applies to projectiles
etc…
Satellites
A satellite is
planet around Sun
moon around planet
artificial satellite around planet
Keppler’s Laws were stated in terms of
planets around Sun
but apply to others, too
Keppler’s Laws
Keppler’s 1st Law
planets travel in elliptical orbit,
link to image
with Sun at one focus
ellipse has 2 foci
 nothing at other focus
larger orbit
larger semi-major axis
more circular
smaller eccentricity
perfect circle
e=0, a=r
Keppler’s Laws
Keppler’s 2nd Law
planet sweeps out equal areas in equal
times,
when closer
PE is ________, so KE is ___
so goes faster when close
when farther
 PE is ________, so KE is ___
so goes slower when far
The same planet goes slower when it is far from the
sun than when it is close to the sun
Satellite Energy
Generally
GMm
E  mv 
r
1
2
2
within one planet’s orbit:
larger r, slower speed
Circular Orbit
uniform circ motion, with Fg=Fc
GM
v 
r
2
GMm
E
2r
Keppler’s Laws
Keppler’s 3rd Law=“Law of Periods”
T2 is proportional to a3,
perfect circle:
F=ma
closer planets go
2
GMm
v
m
2
r
r
GMm
4 r
m 2
2
r
T
2
GM 4
 2
3
r
T
2
GM 4 2
 2
3
a
T
How to Weigh the Sun
Observe planet
the period
and
or
Calculate the mass of the Sun
GM 4
 2
3
a
T
2
Geosynchronous Orbits
Artificial satellite
if it is to keep over same point,
T =
also M =
so
2
GM 4
 2
3
r
T
All circular geosynchronous orbits are at
r = 42000 km
h = 36,000 km
Planet’s Gravity
What is the gravitational pull of a planet
on something on its surface?
let M = planet’s mass, m = object’s mass
R = radius of planet
GMm
Fg  
2
R
Planet’s Gravity
What is the gravitational acceleration
on a planet’s surface?
let ag = free-fall acceleration on planet
free-fall —>
F = ma
GM
ag   2
R
on Earth:
 M = 5.98X1024 kg, R = 6.37X106 m
Earth’s Gravity
What is the gravitational acceleration
on a Earth’s surface?
ag = 9.83 m/s2
g = 9.80 m/s2
????
Force of gravity provides force for
centripetal
and
ag= g +
h