# Orbits of Planets & Satellites

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## Video Clips

#### Planets in Circular Orbits

RealVideo®
4:56 minutes (12:21 - 17:17)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Centripetal Force (6:21 of V5)

#### Escape Velocity and Circular Orbits

RealVideo®
6:56 minutes (0:00 - 6:56)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Energy (17:00 of V11)

#### Circular Orbit Examples

RealVideo®
6:41 minutes (6:56 - 13:37)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Circular Orbits (beginning of V14)

#### Earth-Sun Gravitational System

RealVideo®
6:53 minutes (32:37 - 39:30)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Gravitation (31:11 of V11)

#### Kepler's Laws

RealVideo®
10:09 minutes (0:00 - 10:09)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Calculating Semi-major Axis and Period

RealVideo®
7:14 minutes (10:09 - 17:23)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Kepler's Laws (beginning of V22)

#### Velocity at Apogee and Perigee

RealVideo®
6:49 minutes (17:23 - 24:12)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Calculating Semi-major Axis and Period (10:09 of V22)

#### Changing Orbits

RealVideo®
3:57 minutes (24:12 - 28:09)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Elliptical Orbits (beginning of V22)

#### Passing a Ham Sandwich I

RealVideo®
11:28 minutes (28:02 - 39:30)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Changing Orbits (24:12 of V22)

#### Passing a Ham Sandwich II

RealVideo®
9:36 minutes (39:30 - 49:06)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Passing a Ham Sandwich I (28:02 of V22)

## Lecture Notes

#### Planetary Motion I

PDF - 1.6 MB
Page 4 to page 6

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Gravitational Forces

#### Planetary Motion II

PDF - 1.5 MB
Page 1 to page 6

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 28

#### Planetary Motion I

PDF
Page 10 to page 20

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Gravitational Forces

#### Planetary Motion II

PDF
Page 1 to page 19

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 28

#### Angular Momentum of Orbits

PDF#
Page 1

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

Prior Knowledge: Moment of Inertia

#### Kepler's Laws and Planetary Motion

PDF#
Page 10 to page 29

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.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 26

## Practice Problems

#### (8.01L, Fall 2005)

PDF
Problem 1

Motion of spacecraft in orbit around a planet.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Circular Orbits

PDF
Problem 1

Motion of spacecraft in orbit around a planet.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Period of the Moon

PDF
Problem 15

Modeling the orbit of the moon and finding its period.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Planet Orbiting a Star

PDF
Problem 16

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Synchronous Satellite

PDF
Problem 1

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Gravitational Potential and Kinetic Energy

PDF
Problem 1

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Satellite Launch

PDF#
Problem 1

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Going to the Sun

PDF#
Problem 3

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Very Elliptical Orbit

PDF#
Problem 1h

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### Conservation of Energy

PDF#
Problem 11

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

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Elliptic Orbit

PDF
Problem 5

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Planetary Orbits

PDF
Problem B5

Elliptical orbit of a comet around the sun.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Binary Star System

PDF#
Problem 3

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Elliptical Orbit

PDF#
Problem 9

Speed and energy at apogee for elliptically orbiting satellite.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None