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

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

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

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

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

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

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

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

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

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

Circular orbits; elliptical orbits with example; 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.

Circular orbits; elliptical orbits with example; 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.

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.

Motion of spacecraft in orbit around a planet.

Motion of spacecraft in orbit around a planet.

Modeling the orbit of the moon and finding its period.

Solution (PDF)^#

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

Solution (PDF)^#

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

Solution (PDF)^#

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

Solution (PDF)^#

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

Solution (PDF)^#

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

Solution (PDF)^#

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

Solution (PDF)

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

Solution (PDF)

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

Solution (PDF)

Elliptical orbit of a comet around the sun.

Solution (PDF - 2.0 MB)

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

Solution (PDF)

Speed and energy at apogee for elliptically orbiting satellite.

Solution (PDF)^#

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

Solution (PDF)