Unit 13: Gravitation
Newton's law of gravitation, Kepler's laws as its consequence, and the escape velocity that separates an orbit from a launch.
6 topics · 21 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Newton's Law of Universal Gravitation
- How it worksHow does gravitational force fall off with the square of the distance between two masses?
- Worked exampleFind the gravitational force between two 1000 kg masses 2 m apart, using G = 6.674e-11 N m2/kg2.
- Common mistakeWhy doesn't doubling the distance between two masses just cut the gravitational force between them in half?
Your turn1 of 2
Two masses of 3634 kg and 3420 kg are 9 m apart. Using G = 6.674e-11 N m2/kg2, what is the gravitational force between them, in newtons?Gravitational Field and g
- How it worksHow does dividing gravitational force by mass turn Newton's law into a field filling the space around a planet?
- Worked exampleFind the acceleration due to gravity at the surface of a planet with mass 5e24 kg and radius 6e6 m.
- Common mistakeWhy doesn't the value of g at a planet's surface depend on the mass of the object that's falling?
- Going furtherWhat happens to the value of g as you climb from Earth's surface up to twice Earth's radius?
Your turn1 of 2
A planet has mass 6.482085e+24 kg and radius 6595976 m. Using G = 6.674e-11 N m2/kg2, what is the acceleration due to gravity at its surface, in meters per second squared?Kepler's Laws of Planetary Motion
- How it worksHow does Kepler's second law, equal areas swept in equal times, follow directly from conservation of angular momentum?
- How it worksHow does Kepler's third law link an orbit's period to its average distance from the Sun?
- Worked exampleFind the orbital period of a planet with an orbital radius 4 times Earth's, using Kepler's third law.
- Common mistakeWhy isn't every planetary orbit a perfect circle, given that gravity pulls symmetrically in every direction?
Your turn1 of 2
A planet orbits at 6.72 times Earth's orbital radius. Using Kepler's third law, what is its orbital period, in years?Circular Orbits and Orbital Mechanics
- How it worksHow does setting gravitational force equal to the required centripetal force pin down a satellite's orbital speed?
- Worked exampleFind the orbital speed of a satellite 400 km above Earth's surface, using Earth's radius 6.37e6 m and mass 5.97e24 kg.
- Common mistakeWhy isn't an astronaut in orbit actually floating in a region where gravity has stopped acting on them?
Your turn1 of 2
A satellite orbits 787 km above a planet's surface. Using the planet's radius 6298 km and mass 6.796699e+24 kg (G = 6.674e-11), what is its orbital speed, in meters per second?Gravitational Potential Energy and Escape Velocity
- How it worksHow does setting total mechanical energy to zero at infinity define the escape velocity from a planet?
- Worked exampleFind the escape velocity from a planet with mass 6.4e23 kg and radius 3.4e6 m.
- Common mistakeWhy doesn't escape velocity depend on the direction or angle an object is launched at?
- Going furtherWhat happens to the escape velocity needed from a planet as its radius shrinks while its mass stays fixed?
Your turn1 of 2
A planet has mass 7.178502e+23 kg and radius 3946982 m. Using G = 6.674e-11 N m2/kg2, what is the escape velocity from its surface, in meters per second?Energy of Orbits and Black Holes
- How it worksHow does the total energy of a bound orbit staying negative explain why the orbiting object never escapes?
- Worked exampleFind the Schwarzschild radius of an object with Earth's mass, 5.97e24 kg, using r = 2GM/c2.
- Ties togetherHow does the escape velocity formula for an ordinary planet turn into the definition of a black hole's event horizon?
Your turn1 of 2
An object has mass 6.571336e+24 kg. Using r = 2GM/c2 with G = 6.674e-11 and c = 3e8 m/s, what is its Schwarzschild radius, in meters?