Transcript Planet Radius Period

And Newton’s Mathematical Synthesis
Tycho Brahe
(1546-1601)
• Records
meticulous info.
about planets.
It doesn’t seem so hard… or does it?
What He Saw
Johannes Kepler
Johannes Kepler
(1571 – 1630)
• Planets follow elliptical paths with the
sun at one foci.
• Planets sweep out equal areas in equal
amounts of time.
http://home.cvc.org/science/kepler.gif
Planet
Radius
(AU)
Mercury .390
Venus
.720
Earth
1.00
Mars
1.52
Jupiter
5.20
Saturn
9.54
Uranus
19.18
Neptune 30.06
Pluto
39.44
DATA:
Kepler recognized
that the period of a
planet was
proportional to its
distance from the
sun… What was his
finding???
1 AU -- “Astronomical Unit”
2
T
=
3
R
Period
(years)
.241
.615
1.00
1.88
11.8
29.5
84.0
165
248
Newton’s Synthesis
Kepler’s laws can be derived from Newton’s
equation for universal gravitation
ΣF = m1 a
Fg = G m1 m2
r2
Einstein’s Problem with Newton’s Gravity
PBS – Elegant Universe
Time and Space are bound together in a 4-D
“fabric” that is warped by the presence of mass!
http://www.unm.edu/~physics/demo/html_demo_pages/8c2010.jpg
Warped Space-Time:
Huge mass = huge …
What does light do?
Fighting Gravity in a Star… loosing to gravity…
“Black Hole”-
Singularity -
Event Horizon -