1 / 0

Universal Gravitation

Universal Gravitation. Motion in the heavens and on Earth. Kepler’s laws of planetary motion- Used Brahe’s data from planetary observations Three laws were developed to explain planetary motion and satellite motion. Kepler’s 1 st Law.

peggy
Download Presentation

Universal Gravitation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Universal Gravitation

  2. Motion in the heavens and on Earth Kepler’s laws of planetary motion- Used Brahe’s data from planetary observations Three laws were developed to explain planetary motion and satellite motion
  3. Kepler’s 1st Law Paths of planets are ellipses with the center of the sun at one focus The planet paths are near circular but are in fact ellipses Refers to a single planet/satellite/moon in orbit around the sun
  4. Kepler’s 2nd Law An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Planets move fastest when closest to the sun and slowest when farthest away. Figure 8-2 shows the graphic representation of this law Refers to a single planet/moon/satellite revolving around the sun
  5. Kepler’s 3rd Law The ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratio of the cubes of their average distances from the sun. Ta = period of planet a Tb = period of planet b ra= average distance of planet a from sun rb = average distance of planet b from sun
  6. Kepler’s 3rd Law cont. (Ta/Tb)2 = (ra/rb)3 This law refers to several satellites around a single body- the planets/moons/satellites around the sun
  7. Practice #1 Galileo discovered four moons of Jupiter, Io, which he measured to be 4.2 units from the center of Jupiter, has a period of 1.8 days. He measured the radius of Ganymede’s orbit as 10.7 units. Use Kepler’s third law to find the period of Ganymede.
  8. Practice #1
  9. Practice #2 An asteroid revolves around the sun with a mean orbital radius twice that of earth’s. Predict the period of the asteroid in earth years.
  10. Practice #2
  11. Universal Gravitation Isaac Newton expanded Kepler’s 1st law to include that if the orbit was in fact elliptical, then the net force on the planet varied inversely to the square of the distance between the planet and the sun. F is proportional to 1/d2 where d is the average distance between the center of the two bodies The force is also proportional to the mass of the objects
  12. Universal Gravitation cont. So if force is proportional to the masses (m1 and m2) of two planets and inversely proportional to the square of the distance (d) between the centers of the two planets, then Newton proposed that there must also be a universal constant (G)- something that is the same everywhere. He devised the equation: F = G(m1m2/d2)
  13. Universal Gravitation cont. Newton used this equation and his second law of motion to calculate the period of the earth: Tp2 = (4π2/GMs) rps3 Tp = period of the planet G = universal constant Ms = mass of the sun rps = radius of the planets orbit
  14. The weight of the Earth Cavendish determined the gravitational constant (G) = 6.67 x 10-11 N*m2/kg2 Cavendish devised a way to determine the mass of the Earth using Newton’s law of gravitation or F = mg Me = (gre2) / G
More Related