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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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