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MOTION IN SPACE

MOTION IN SPACE. KEPLER’S LAWS. In 1543 Copernicus published On the Revolutions of the Heavenly Spheres in which he proposed that Earth and the other planets orbit the sun in perfect circles

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MOTION IN SPACE

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  1. MOTION IN SPACE

  2. KEPLER’S LAWS • In 1543 Copernicus published On the Revolutions of the Heavenly Spheres in which he proposed that Earth and the other planets orbit the sun in perfect circles • The astronomer Tycho Brahe made many precise observations of the planets and the stars, but some of his data did not agree with the Capernican model.

  3. Johannes Kepler, an astronomer, worked for many years to reconcile Copernican theroy with Brahe’s data. • His analysis led to three laws of planetary motion • These laws were developed a generation before Newton’s law of universal gravitation

  4. THE THREE LAWS • FIRST LAW- Each planet travels in an elliptical orbit around the sun, an the sun is at one of the focal points • The first law states that the planet’s orbits are ellipses rather than circles • He came about this lab while trying to make sense of Mars’ orbit • He experimented with 70 different circles and finally realized an ellipse with the sun at a focal point fit the data perfectly

  5. SECOND LAW- An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time interval • “Law of equal areas” • If the time it takes a planet to travel the arc of section c (tc), is equal the time is takes to travel the arc in section b (tb), then the area Ac is equal to the area Ab • Planets travel faster when they are closer to the sun

  6. THIRD LAW- The square of a planet’s orbital period (T2) is proportional to the cube of the average distance (r3) between the planet and the sun, or T2αr3 • Relates the orbital periods and distances or one planet to those of another planet • The orbital period (T) is the time it takes to finish one full revolution • This law also applies to satellites orbiting the Earth

  7. According to Newton’s Third law, T2 α r3, the constant of proportionality between the two turns out to be 4π2/Gm • Where m is the mass of the central object • Thus, Kepler’s Third law can also be stated:

  8. PERIOD AND ORBITAL SPEED EQUATIONS • Solving for orbital period: • SPEED OF AN OBJECT IN CIRCULAR ORBIT: • In both cases m is the mass of the central object

  9. Sample problem • During Magellan’s fifth orbit around Venus, it traveled at a mean altitude of 361 km. If the orbit had been circular, what would Magellan’s period and speed have been? • Given: r1=361 km=3.61 x 105 m • T=? v=?

  10. Solution • Radius of venus : r2=6.05 x 106 m • Mass of venus: m=4.87x1024 kg • r=r1+r2=6.41 x 106 m • T=5.66 x103 s • Vt = 7.12 x 103 m/s

  11. Weightlessness • This is not the absence of gravity • It is the absence of a support force • An elevator explains this nicely- The sensation of weight is equal to the force that you exert against a supporting floor • When the floor accelerates up or down, your weight seems to vary

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