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Announcements

Announcements.

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Announcements

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  1. Announcements • Exam 1 is next week. Will be similar to homework problems. Bring a scientific calculator. Equations Sheet will be provided (same one you have been using). Posted lectures have worked out solutions to the example problems. Solutions to all but the HW assigned today will be posted by Friday afternoon. • Homework Set 4: Chapter 3 #35, 39, 40, 45 & 47 • Don’t forget to give me your schedule with this week’s homework so we can find an alternate date for the project presentations.

  2. In addition to his three laws of motion, Newton formulated the Universal Law of Gravity G is the universal gravitational constant (6.67 x 10-11 ), m1 and m2 are the masses of the two objects, r1-2 is the distance between them and is the direction of the line connecting the two masses.

  3. Easy example Using the information in the Appendix, determine the gravitational force of the Earth on the Moon. Which way does it act? What is the gravitational force of the Moon on the Earth? Which way does it act?

  4. Solution ME = 5.97 x 1024 kg MM = 7.35 x 1022 kg rE-M = 3.844 x 105 km Gravity is always an attractive force so the Earth pulls on the Moon: the direction is from the Moon to the Earth. The force of the Moon on the Earth is exactly the same but in the opposite direction (Newton’s 3rd Law) 1.98 x 1020 N directed from the Earth to the Moon

  5. Newton derived Kepler’s 3rd Law using universal gravitation and his laws of motion Rearranges to give Where M* is the total mass of the system. For a planet orbiting a star, this is effectively the mass of the star. For a moon or satellite orbiting a planet this is effectively the mass of the planet unless the moon is large.

  6. Newton’s form of Kepler’s 3rd Example The two moons of Mars, Phobos and Deimos, orbit the planet at 9,380 km and 23,460 km respectively. If their periods are 0.32 days (Phobos) and 1.26 days (Deimos), what is the mass of Mars? The equation to use has “G” in it which has units of (Nm2/kg2) so the 1st thing to do is unit conversions: km to m and days to seconds

  7. Newton’s form of Kepler’s 3rd example continued Within round-off error of being the same. The textbook value is 6.42x1023 kg

  8. Newton’s form of Kepler’s 3rd Problems The first extra-solar planet discovered orbits the star 51 Pegasi. If the semimajor axis is 0.052 AU and the orbital period is 4.23 days, what is the mass of 51 Pegasi? Triton, the largest moon of Neptune, orbits the planet at a distance of 3.548x105 km every 5.88 days. Use this information to determine the mass of Neptune.

  9. Example 1 Solution 1 Using units of AU and years, the ratio of the cube of the semimajor axis to the square of the orbital period will give the mass in solar masses. So, we only need to convert the period from days to years. Now use the ratio of A3 to P2 to find the mass in solar masses

  10. Example 1 Solution 2 Since G has units of (Nm2/kg2), distances must be in meters and periods in seconds so do unit conversions first Next, chose the equation to use and algebraically solve it for the mass. Finally, plug in numbers to solve

  11. Example Solution 2 Do unit conversions first Use the same equation as the previous example

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