Transcript Kepler`s First Law

Kepler’s Three Laws
Kepler’s First Law
• The orbit of a
planet about the
Sun is an ellipse
with the Sun at
one focus.
Kepler’s First Law
Planets revolve around the sun in
elliptical orbits with the sun located
at one focus of the ellipse
planet
sun
+
focus
center
focus
Earth’s orbit
A
Sun
P
• Terminology
Perihelion (P):
• Earth’s closest point to Sun (January 2nd)
• d = 147.1 x 106 km
Aphelion (A):
• Earth’s most distant point (July 4th)
• d = 152.1 x 106 km
3% variation in Earth’s distance from the Sun
Kepler’s Second Law
• A line joining
a planet and
the Sun
sweeps out
equal areas in
equal intervals
of time.
Kepler’s Second Law
The line from the sun to a planet sweeps
out equal areas in equal time
intervals. t
1
t2
areaA
t4
aphelion
(slowest)
areaB
areaA = areaB if t2-t1 = t4-t3
t3
perihelion
(fastest)
Elliptical
path/orbit
followed by
planet
Sun
+
◦
Kepler’s Third Law
• The square of a planet's
orbital period is
proportional to the cube
of the length of its
semimajor axis.
• Or simply… T2 = R3
if T is measured in years
and R is measured in
astronomical units.
Kepler’s Third Law
For any two planets, the ratio
of their mean distance from
the sun cubed equals the
ratio of their orbital
periods squared.
Planets far from the sun take
longer to orbit the sun than do
planets nearer the sun.
Kepler's Third Law
The greater the
distance from
the sun, the
longer the
period of
revolution.
Two reasons:
•Longer orbits
•Slower orbital
velocities.
Mars – 228 mill. Km,
687 days
Earth – 150 mill. Km,
365 days
Not drawn to scale.
Kepler’s Laws
1. Planets move on elliptical orbits
2. The planet’s radius-vector sweeps
out the same areas in equal times
3. The squares of the periods of the
planets are proportional to the
cubes of their semi-major axes
Kepler’s Laws...Simply
• Law 1: Elliptical orbits…
• Law 2: Equal areas in equal times…
• Law 3: T2 = R3 (Further, longer …)
http://www.geocities.com/rockhead2333/257,13,Slide 13
http://www.hannibal.cnyric.org/TeacherWebs/Toneil/power%20point/296,41,Structure of the Universe