- Planets in Circular Orbits
- Escape Velocity and Circular Orbits
- Circular Orbit Examples
- Earth-Sun Gravitational System
- Kepler's Laws
- Calculating Semi-major Axis and Period
- Velocity at Apogee and Perigee
- Changing Orbits
- Passing a Ham Sandwich
- Planetary Motion
- Angular Momentum of Orbits
- Kepler's Laws and Planetary Motion

Uniform circular motion calculations for planets, and graph showing that a_{c}, and thus gravity, falls off as 1/R^{2}.

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 5 (12:21 - 17:17)
Planets in Circular Orbits

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 14 (0:00 - 6:56)
Escape Velocity and Circular Orbits

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 14 (6:56 - 13:37)
Circular Orbit Examples

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 18 (32:37 - 39:30)
Earth-Sun Gravitational System

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 22 (0:00 - 10:09)
Kepler's Laws

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 22 (10:09 - 17:23)
Calculating Semi-major Axis and Period

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 22 (17:23 - 24:12)
Velocity at Apogee and Perigee

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 22 (24:12 - 28:09)
Changing Orbits

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

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)
Passing a Ham Sandwich I

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

- Watch video clip from Lecture 22 (39:30 - 49:06)
Passing a Ham Sandwich II

8.01

*Physics I*, Fall 2003

Prof. Stanley Kowalski

**Course Material Related to This Topic:**

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.

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

**Course Material Related to This Topic:**

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.

8.01T

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

Motion of spacecraft in orbit around a planet.

8.01L

*Physics I: Classical Mechanics*, Fall 2005

Dr. George Stephans

**Course Material Related to This Topic:**

- Complete practice problem 1

Modeling the orbit of the moon and finding its period.

8.01T

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete practice problem 15
- Check solution to practice problem 15

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

8.01T

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete practice problem 16
- Check solution to practice problem 16

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

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete practice problem 1
- Check solution to practice problem 1

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

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete practice problem 1
- Check solution to practice problem 1

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 1
- Check solution to practice problem 1

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 3
- Check solution to practice problem 3

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

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 1h
- Check solution to practice problem 1h

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

8.01L

*Physics I: Classical Mechanic*s, Fall 2005

Dr. George Stephans

**Course Material Related to This Topic:**

- Complete exam problem 11
- Check solution to exam problem 11

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

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete exam problem 5
- Check solution to exam problem 5

Elliptical orbit of a comet around the sun.

*Physics I*, Fall 2004

Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow

**Course Material Related to This Topic:**

- Complete exam problem B5
- Check solution to exam problem B5

5-part binary star problem; calculating F_{g}, a, T.

- 8.01
*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete exam problem 3
- Check solution to exam problem 3

Speed and energy at apogee for elliptically orbiting satellite.

8.01X

*Physics I: Classical Mechanics with an Experimental Focus*, Fall 2002

Dr. Peter Dourmashkin, Prof. Kate Scholberg

**Course Material Related to This Topic:**

- Complete exam problem 9
- Check solution to exam problem 9

4-part elliptical orbit problem; finding apogee v, total energy, v_{0}.

8.01

*Physics I: Classical Mechanics*, Fall 1999

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete exam problem 7b–7e
- Check solution to exam problem 7b–7e