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Universal Gravitation and Kepler's Laws: Review of Lecture 25

This review summarizes the key topics covered in Lecture 25, including universal gravitation, Kepler's Laws, projectiles, escape velocity, and more. Learn about the laws that govern planetary motion and how to calculate the mass of the Sun. Explore the concept of geosynchronous orbits and understand the behavior of projectiles near a planet's surface. Discover the significance of escape velocity and the characteristics of black holes. This summary provides a concise overview of the lecture material.

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Universal Gravitation and Kepler's Laws: Review of Lecture 25

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  1. PH 201 Dr. Cecilia Vogel Lecture 25

  2. REVIEW • universal gravitation • Force & PE • accel of grav • orbits OUTLINE • universal gravitation • Kepler’s 3rd Law • Generalize projectiles • Escape velocity

  3. Keppler’s Laws • Keppler’s 1st Law • planets travel in elliptical orbit, • with Sun at one focus • Keppler’s 2nd Law • planet sweeps out equal areas in equal times

  4. Keppler’s Laws • Keppler’s 3rd Law=“Law of Periods” • T2 is proportional to a3, • perfect circle: • F=ma • closer planets go

  5. How to Weigh the Sun • Observe planet • the period • and • or • Calculate the mass of the Sun

  6. Geosynchronous Orbits • Artificial satellite • if it is to keep over same point, • T = • also M = • so • All circular geosynchronous orbits are at • r = 42000 km • h = 36,000 km

  7. Projectiles • Projectile near planet’s surface • behave like constant • Projectiles going high • accel varies • often can use energy conservation • Applies to projectiles going • or • or • so long as no

  8. Projectile Example Rocket projected upward from moon’s surface at a speed of 100 m/s. How high will it go, before it begins to fall back?

  9. Escape Velocity • escape velocity is speed • Initial • r = R, v = vE • Final • r = ∞, v = 0 • Not in orbit, don’t use orbit eqn!!!!

  10. Black hole • Light cannot escape • if escape velocity =

  11. Summary • Kepler’s Laws • ellipse, foci, semi-major axis, periods • Projectiles still conserve energy, • but U is not mgh • Escape velocity – zero mechanical energy

  12. PAL • Imaginary planet has a mass of 1024 kg, a radius of 108 m. • Find the acceleration of gravity on the planet’s surface. • What initial speed must a rocket have to reach a height of 3X108 m? • Find the escape speed of this planet. • G=6.67X10-11 Nm2/kg2.

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