So before we start, if you get this answer wrong, leave a comment about your thinking. Some of you may get it wrong and still not want to comment. Before we get to the answer, let’s review basic orbital mechanics, but simplified.
Orbital mechanics
Johannes Kepler did remarkable research into Orbital Mechanics. Based on the data collected by Tycho Brahe without the aid of a telescope, Kepler developed the three laws which became the foundation for Orbital Mechanics. Kepler’s three laws described the motion of the planets across the sky so well that it redefined the established understanding of our universe.
1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.
3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
Kepler’s laws were based on the observed data of the motion of the planets as viewed from Earth. The laws also can be applied to satellites orbiting other objects as well such as the International Space Station orbiting the Earth in Low Earth Orbit or a Geostationary satellite.
So the reason why Kepler’s laws work is Gravity. One of the focal points of the elliptical orbit is a mass. Like in the first law, that focal point is our sun. For other orbits, the focus point can be the Earth, the Moon etc.
Now that we had a chance to review over the basics of Orbital Mechanics, can a satellite orbit around nothing. Can a satellite orbit around a focus point with no mass? If you follow the three laws of orbital mechanics then the answer is no.
Now that you have your answer firmed up in your head, now we need to consider another famous
Every law has a loophole. Enter the loophole for Orbital Mechanics, the Lagrangian point.
The Lagrange Points reflect positions where the gravitational pull of two large masses is balanced out by the centripetal force required for a small object to move with them. Lagrange proposed this in his “General Three-Body Problem” in his award winning paper (Essai sur le Problème des Trois Corps, 1772).
Specifically, there are five Lagrangian points (L1-L5) in an orbital configuration. A small object like a satellite can be stationary relative to two larger objects like the Sun and the Earth. Lissajous orbits are, in theory, highly stable. In practice, orbits around a Lagrangian point is dynamically unstable. Small departures from equilibrium grow quickly as time passes. A spacecraft located in an orbit around any libration point needs propulsion systems for periodic orbital corrections.
This unique orbits are sometimes called Lissajous orbits. And yes, NASA and ESA have used Lagrange points for missions.
Finding the Lagrange Points
NASA did a good job explaining Lagrange points in terms that most of us can understand. Think of them in much the same way that wind speeds can be viewed on a weather map. The wind force is strongest where the contours are close together and weak when the lines are far apart.
L4 and L5 are similar to hilltops and L1, L2 and L3 correspond to valleys. Satellites placed at the Lagrange points will have a tendency to wander off over time. A satellite parked at L4 or L5 starts to flow in the direction of the next line. At this point, the Coriolis force comes into play. Yes, these are the same force that causes hurricanes to spin upon the earth also sends the satellite into a stable orbit around the Lagrange point.
