Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Kepler’s Laws
Planetary & Satellite Motion
History – Johannes Kepler
Born in Germany in 1571
Assistant to Tycho Brahe (Danish)
• Brahe, as an astronomer, meticulously
•
gathered planetary data
Kepler analyzed Brahe’s Mars data and
postulated 3 foundation laws of planetary
motion (1609+)
Kepler’s First Law - Ellipses
Planets move in elliptical orbits with the
Sun as one of the foci
Kepler’s Second Law – Equal
Areas
A line from the Sun to a planet sweeps
out equal areas in equal times
...
67 x 10-11 N-m2/kg2
• M = mass of the foci body (ex, Sun)
Practice Kepler’s 3rd Law
What is the orbital period (T) of Neptune if
its average orbital radius (R) is 4
...
99e30 kg?
Solve T2 = 4π2/(GM) x R3
• T2 = 4π2/(6
...
99e30)*(4
...
70e19
• T = 5
...
21e9 sec
and an average orbital radius (R) of
4
...
Solve: T2/R3
• (5
...
495e12)3
• = 2
...
496 x 1011 meters
• 1 EY = period of Earth
• 1 EY = 365 days = 3
...
6E6 s, R = 5
...
79E10/1
...
387
• EY = 7
...
156E7 = 0
...
79 x 1010 m from
the Sun and has an orbital period of 7
...
• What is the orbital radius (R) in AU?
• R = 5
...
496e11 = 0
...
6e6/3
...
241 EY
• What is the ratio of the orbital period (T)
(squared) to the orbital radius (R) (cubed)
using the AU and EY values?
Kepler Practice
The shuttle orbits the Earth at 400 kms
above the surface
...
37 x 106 m and
5
...
32 days and that the earthmoon distance is 3
...
Solve using K’s 3rd Law: T2= 4π2R3/(GM)
• M = 4π2R3/(GT2 )
• M = 6