Binary Systems & Gravitational Waves
When two massive objects orbit each other, they create ripples in spacetime itself. These gravitational waves travel at the speed of light and carry away energy, causing the orbit to decay.
Einstein's Ripples in Spacetime
When massive objects accelerate, they create waves in the fabric of spacetime itself. These waves were predicted by Einstein in 1915 but only detected 100 years later by LIGO.
Gravitational wave strain amplitude
Kepler's Three Laws of Planetary Motion
Johannes Kepler discovered three fundamental laws that describe how planets move around the Sun. These laws apply to all orbiting bodies, from planets to satellites to binary stars.
First Law: Elliptical Orbits
All planets orbit the Sun in elliptical paths, with the Sun at one focus of the ellipse.
Orbital equation in polar coordinates
Second Law: Equal Areas in Equal Time
A planet sweeps out equal areas in equal time intervals. This means planets move faster when closer to the Sun.
Angular momentum conservation
Third Law: The Harmonic Law
The square of the orbital period is proportional to the cube of the semi-major axis.
Kepler's Third Law
Escape Velocity & Orbital Energy
Understanding orbital energy is key to spaceflight. The escape velocity is the minimum speed needed to break free from a gravitational field and reach infinity.