1. Kepler’s Three Laws

2. Kepler’s First Law
The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

3. Kepler’s First Law
Planets revolve around the sun in elliptical orbits with the sun located at one focus of the ellipse +
focus
center
sun
planet

4. Earth’s orbit Terminology Perihelion (P):
Sun
Terminology
Perihelion (P):
Earth’s closest point to Sun (January 2nd)
d = x 106 km
Aphelion (A):
Earth’s most distant point (July 4th)
d = x 106 km P
3% variation in Earth’s distance from the Sun

5. Kepler’s Second Law
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

6. Kepler’s Second Law
The line from the sun to a planet sweeps out equal areas in equal time intervals. t1
areaA t2 t4
aphelion
(slowest)
perihelion
(fastest)
areaB
areaA = areaB if t2-t1 = t4-t3 t3

7. Speed During Orbit ***Slower at Aphelion(Further away)
***Faster at Perihelion(Closer to)

8. Elliptical path/orbit followed by
planet
Sun + ◦

9. 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.

10. 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.

11. Kepler's Third Law
The greater the distance from the sun, the longer the period of revolution.
Mars – 228 mill. Km, 687 days
Two reasons:
Longer orbits
Slower orbital velocities.
Earth – 150 mill. Km, 365 days
Not drawn to scale.

16. Kepler’s Laws 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

17. Kepler’s Laws...Simply Law 1: Elliptical orbits…
Law 2: Equal areas in equal times…
Law 3: T2 = R3 (Further, longer …)