keplers laws of planetary motion for BS students

Kepler’s laws of planetary motion describe how planets move around the Sun. The first law, the law of ellipses, states that each planet moves in an elliptical orbit with the Sun at one focus. The second law, the law of equal areas, says that a line joining a planet and the Sun sweeps out equal areas in equal intervals of time, meaning planets move faster when closer to the Sun. The third law, the harmonic law, establishes that the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit, showing a precise mathematical relationship between a planet’s distance from the Sun and its orbital time.

1. KEPLER:KEPLER:
the laws of planetary motion
KEPLER’S
FIRST
LAW
KEPLER’S
SECOND
LAW
KEPLER’S
THIRD
LAW
INTERESTING
APPLETS

2. Johannes Kepler
Born on December 27, 1571
in Germany
Studied the planetary motion of
Mars
Used observational data of Brahe
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3. Tyco Brahe
Danish astronomer who hired
Kepler as his assistant
Came up with accurate observations of
Mars with his naked eyes
Assigned Kepler to develop a theory of
planetary motion using his observations
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4. Instruments
Tyco Brahe
only compass and sextant
No telescope – naked eye
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5. Kepler’s FIRST Law
“The orbit of each planet is an
ellipse and the Sun is at one focus”
Kepler proved Copernicus wrong –
planets didn’t move in circles
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6. Ellipse
Elongated & flattened circle
Characterized by eccentricity and
length of major axis
Eccentricity – degree of flatness
Major axis – longer axis
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KEPLER’S
FIRST
LAW

7. Focus
Focus – one of two special points on
the major axis of an ellipse
Foci – plural of focus
A+B is always
the same on
any point on
the ellipse
KEPLER’S
FIRST
LAW
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8. Eccentricity
Eccentricity is the degree of flatness
Eccentricity (e) = 0 is circle
Earth e = 0.017
 e = c/a
 c = center to focus
 a = half of major axis/
semi-major axis
KEPLER’S
FIRST
LAW
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9. Aphelion & Perihelion
Aphelion is the point on the orbit
farthest from the sun
Perihelion is the point on the orbit
closest to the sun
KEPLER’S
FIRST
LAW
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10. Kepler’s SECOND Law
“The line joining the planet to
the sun sweeps out equal areas
in equal intervals of time”
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11. In Another Words…
The area from one time to another
time is equal to another area with
the same time interval
All of the areas (in yellow and
peach) have equal intervals
of time
KEPLER’S
SECOND
LAW
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12. Acceleration of Planets
Planet moves faster when closer to the
sun
Force acting on the planet increases as
distance decreases and planet accelerates in
its orbit
Planet moves slower
when farther
from the sun
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KEPLER’S
SECOND
LAW

13. Kepler’s THIRD Law
“The square of the period of any
planet is proportional to the cube
of the semi-major of its axis”
Also referred to as the Harmonic Law
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14. T²  a³
T = orbital period in years
 a = semi-major axis in astronomical
unit (AU)
Can calculate how long it takes
(period) for planets to orbit if semi-
major axis is known
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KEPLER’S
THIRD
LAW

15. Astronomical Unit
Astronomical unit – AU
AU is the mean distance between
Earth and the Sun
1 AU ≈ 1.5 x 10
8
km ≈ 9.3 x 10
7
miles
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KEPLER’S
THIRD
LAW

16. Examples of 3
rd
Law
Calculating the orbital period of 1AU
T² = a³
T² = (1)³ = 1
T = 1 year
Calculating the orbital period of 4AU
T² = a³
T² = (4)³ = 64
T = 8 years
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KEPLER’S
THIRD
LAW

17. Orbital Data
The orbital data of various planets
Planet
eccentricity
(e)
T (yr) a (AU) T
2
a
3
Mercury 0.206 0.24 0.39 0.06 0.06
Venus 0.007 0.62 0.72 0.39 0.37
Earth 0.017 1 1 1 1
Mars 0.093 1.88 1.52 3.53 3.51
Jupiter 0.048 11.9 5.2 142 141
Saturn 0.056 29.5 9.54 870 868
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18. Comets
Although Kepler’s
laws were intended
to describe the
motion of planets
around the sun, the
laws also apply to
comets
Comets are good
examples because
they have very
elliptical orbits
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19. Kepler’s Three Laws
Orbit of each planet is an
ellipse & Sun is at one focus
Equal areas in equal intervals of
time
T² = a³
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20. Contributions
Kepler’s second law
(equal area) helped
Newton come up with
his Law of Universal
Gravitation
Motions of satellite
and spacecraft in
orbit near planets
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21. Interesting Applets
http://www.fed.cuhk.edu.hk/sci_lab/
ntnujava/Kepler/Kepler.html
http://csep10.phys.utk.edu/astr162/lect/
binaries/visual/kepleroldframe.html
http://www.ioncmaste.ca/homepage/
resources/web_resources/CSA_Astro9/
files/multimedia/unit4/keplers_laws/
keplers_laws.html
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