# Orbits of Planets & Satellites

## Planets in Circular Orbits

Uniform circular motion calculations for planets, and graph showing that ac, and thus gravity, falls off as 1/R2.

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• Watch {}video clip from Lecture 5 (12:21 - 17:17)

## Escape Velocity and Circular Orbits

Calculation of escape velocity as well as velocity and period of circular orbit.

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• Watch {}video clip from Lecture 14 (0:00 - 6:56)

## Circular Orbit Examples

Calculation of v, T for shuttle, moon, Earth, and Jupiter; V and T independent of mass.

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• Watch {}video clip from Lecture 14 (6:56 - 13:37)

## Earth-Sun Gravitational System

Law of universal gravitation; velocity, potential, and kinetic energy for Earth's orbit; escape velocity for Earth.

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• Watch {}video clip from Lecture 18 (32:37 - 39:30)

## Kepler's Laws

Statements of Kepler's three laws of planetary motion; numerical evidence for third law; consequences of third law.

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## Calculating Semi-major Axis and Period

Calculated from initial orbital conditions; exam problemple of Earth orbit solved explicitly.

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• Watch {}video clip from Lecture 22 (10:09 - 17:23)

## Velocity at Apogee and Perigee

Calculation using conservation of angular momentum; velocity and position of apogee and perigee calculated for Earth orbit.

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• Watch {}video clip from Lecture 22 (17:23 - 24:12)

## Changing Orbits

Qualitative description of change from circular to elliptical orbit for changing speed.

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## Passing a Ham Sandwich

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Calculation of speed and trajectory for throwing sandwich between two spacecraft in same orbit; finding infinite number of solutions.

• Watch {}video clip from Lecture 22 (28:02 - 39:30)

Computer simulation of several possible trajectories for the sandwich, including several failures.

• Watch {}video clip from Lecture 22 (39:30 - 49:06)

## Planetary Motion

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Circular orbits; elliptical orbits with exam problemple; escape velocity; general planetary motion; kinetic energy and momentum of two-particle systems.

Conservation of energy and momentum of orbiting bodies; characteristics of circular, elliptical, hyperbolic, and parabolic orbits; Kepler's Laws, with example.

## Angular Momentum of Orbits

Equations for angular momentum of orbiting bodies; connection of angular momentum and rotational energy to equation of orbit.

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## Kepler's Laws and Planetary Motion

Kepler's laws defined; description of Kepler two body problem; reduction of two body problem and solution of one body problem; energy diagram of circular, elliptic, parabolic, and hyperbolic orbits; equations for position, energy, and angular momentum of an orbiting body; properties of an ellipse; Kepler's equal area law defined; Kepler's law for period of orbit.

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## Circular Orbits

Motion of spacecraft in orbit around a planet.

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## Period of the Moon

Modeling the orbit of the moon and finding its period.

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## Planet Orbiting a Star

Motion of a planet orbiting a star through a cloud of dust.

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## Synchronous Satellite

Finding the radius of the orbit of a synchronous satellite that circles the earth.

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## Gravitational Potential and Kinetic Energy

Energy required to change a satellite's orbit from circular to elliptical.

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## Satellite Launch

Finding initial velocity for satellite launched with given acceleration and angle.

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## Going to the Sun

7-part orbit problem; finding impulses to allow spacecraft to reach sun.

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## Very Elliptical Orbit

Short qualitative problem about when to fire engines for reentry in elliptical orbit.

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## Conservation of Energy

Motion of a small mass launched from the surface of the earth.

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## Elliptic Orbit

Motion of a satellite in an elliptical orbit around a planet.

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## Planetary Orbits

Elliptical orbit of a comet around the sun.

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## Binary Star System

5-part binary star problem; calculating Fg, a, T.

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## Elliptical Orbit

Speed and energy at apogee for elliptically orbiting satellite.

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## Bound Orbit

4-part elliptical orbit problem; finding apogee v, total energy, v0.

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