We learned about orbital motion in a previous lesson. Now that we've also learned about energy, let's apply that to orbital motion.

There are no new types of energy here, just kinetic energy and gravitational potential energy. Using the equation that we derived for orbital speed we can find the kinetic energy of an object in orbit. And if we know the radius of the orbit, we can find the gravitational potential energy of the object-planet system. If we add those together and apply the law of conservation of energy: the total kinetic and gravitational potential energy of an object in orbit is constant over time. The amount of each type of energy may change, but the total will stay the same.

This is obvious for circular orbits: the orbital speed and the orbital radius are constant, so the kinetic energy and gravitational potential energy are constant. But what if the orbit isn't a circle? What if the distance between the object and the planet changes over time? That means the orbit is an ellipse.

By using the conservation of energy we can figure out a lot of different things about an object in orbit: its mass, its speed, the distance between the object and the planet, and the mass of the planet. We can also use it to find something new: the escape velocity required for an object to escape the gravity of a planet.

Multiple-Choice Questions

Answers

Free-Response Questions

Circular motion

• 2024 Q1 - - Block sliding on a track with loops, forces, FBDs, circular motion, energy
• 2023 Q3 - - Block and spring rotating about axle, circular motion, centripetal force, FBDs
• 2018 Q1 - - Spacecraft in circular orbit, circular motion, forces, FBDs, law of gravitation

Law of gravitation

• 2024 Q4 - - Pendulum on different planets, law of gravitation, simple harmonic motion, work, spring force
• 2022 Q2 - - Gravitational force between planet and moons, law of gravitation, FBD's
• 2018 Q1 - - Spacecraft in circular orbit, circular motion, forces, FBDs, law of gravitation

• Matt Anderson - Energy in Orbit
• Flipping Physics - Mechanical Energy of a Satellite in a Circular Orbit
• Matt Anderson - Escape Velocity

• Matt Anderson - Energy of Space Shuttle in Orbit
• Matt Anderson - Energy for Space Shuttle to Change Orbits
• Organic Chemistry Tutor - Escape Velocity

• Smarter Every Day - How to Fly a Spaceship to the Space Station
• Space Flight: The Application of Orbital Mechanics

• Orbits
• Elliptical Orbits & Kepler's 2nd Law
• Two-body problem simulator

We learned about orbital motion in a previous lesson. Now that we've also learned about energy, let's apply that to orbital motion.

There are no new types of energy here, just kinetic energy and gravitational potential energy. Using the equation that we derived for orbital speed we can find the kinetic energy of an object in orbit. And if we know the radius of the orbit, we can find the gravitational potential energy of the object-planet system. If we add those together and apply the law of conservation of energy: the total kinetic and gravitational potential energy of an object in orbit is constant over time. The amount of each type of energy may change, but the total will stay the same.

This is obvious for circular orbits: the orbital speed and the orbital radius are constant, so the kinetic energy and gravitational potential energy are constant. But what if the orbit isn't a circle? What if the distance between the object and the planet changes over time? That means the orbit is an ellipse.

By using the conservation of energy we can figure out a lot of different things about an object in orbit: its mass, its speed, the distance between the object and the planet, and the mass of the planet. We can also use it to find something new: the escape velocity required for an object to escape the gravity of a planet.

Multiple-Choice Questions