Tag Archives: astronomy

The Big Bang Theory of Trojan Asteroids

Season 06, Episode 03: “The Higgs Boson Observation”

In “The Higgs Boson Observation”, we learn that the subject of graduate student and Sheldon’s (Jim Parsons) new assistant, Alex Jensen (Margo Harshman), is on Trojan asteroids at the Earth-Sun L5 Lagrange point. This also happens to be Raj’s (Kunal Nayyar) area of expertise. But what exactly are Trojan asteroids and why are they of interest to astronomers and astrophysicists?

Trojans are minor planets or satellites that share an orbit with a planet but does not collide with it because it orbits around one of the two stable Lagrangian points (trojan points). The L4 and L5 lie approximately 60° ahead of and behind the larger body, respectively .

Area of Research

Trojan Asteroids


There are five points on or near Earth’s orbit known as Lagrange points where an asteroid will remain stationary with respect to Earth as it orbits around the Sun. These points mark the positions where the combined gravitational pull of two large bodies, such as the Earth and the Sun, provides the centripetal force needed to orbit with them.

The Lagrangian points are approximate solutions to what is known as the three-body problem, a famous problem that attempts to model the motion of three bodies as they gravitationally affect each other. In essence, this problem dates back to 1687 when Sir Isaac Newton first published his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), often referred to as simply the “Principia”. Several scientists and mathematicians have all attempted to find an analytical solution to the problem or a simple equation that would describe the motions of all three bodies.

The three-body problem is difficult to solve because the three bodies tug against each other in chaotic and unpredictable ways. Only by simulating the problem on a computer can we see the objects paths. In comparison, the quantum three-body problem is relatively easy to solve and understand. However, approximate solutions can be useful. If the third mass is taken to be small enough that it does not affect the other two masses some interesting solutions crop up.

Celestial Mechanics

To better understand how celestial bodies move in our solar system, we turn to Newton’s law of universal gravitation. This law states that every mass in the Universe attracts every other mass with a force that is proportional to the product of their masses. If we had two masses, \(M_{1}\) and \(M_{2}\), then the force between them would be proportional to the product of the two masses.
\[F \propto M_{1}M_{2}\]
This law also states that the force decreases with the square of the distance between them.
\[F \propto \frac{1}{r^{2}}\]
We can combine these into one equation that will help is analyze and solve the movement of celestial bodies anywhere in the Universe.
where \(G\) is the gravitational constant. This law was deduced by Newton from observations and was formulated in the Principia.

If we were to look at the Sun and Earth system, we would have what is known as the two-body problem. While we may think this is a simple problem but in reality it isn’t. The Earth does not revolve around the Sun as if the more massive Sun was a stationary body but rather both the Earth and Sun revolve around a common point — the center of mass or barycenter. Though makes the problem a little more difficult, as this point is very close to the center of the Sun and we can make an approximation where the Sun is in the center and doesn’t move while the Earth moves around it.

If we use this technique, we can derive an equation that describes the Earth’s motion around the Sun. This is a classic “two-body” problem and its solutions describe the familiar elliptical orbits of the planets known since the time of Kepler. Unfortunately, when we add a third body to our equations of motion, such as a spacecraft lost in space between the Earth and the sun, we can no longer find an analytical solution; the equations become unsolvable.

While the three-body problem has no analytical solution, Joseph-Louis Lagrange in 1772 showed that if we restricted the mass of the third body to be so small that it couldn’t affect the other two, there were some solutions to be found. The solutions to this “restricted three-body problem” finds that the three bodies move in unison and always maintain the same position relative to each other.

These five points, where the third body stays in the same relative point in space, are known as Lagrange points and mark the positions where the combined gravitational pull of the two large masses precisely provides the force to orbit with them. They are labelled L1, L2, L3, L4 and L5 and also known as L-points or libration points.

The Trojan Asteroids

The L4 and L5 libration points lie on the corners of two equilateral triangles. The points are balanced because the gravitational forces between the Earth and Sun keep any object in orbital equilibrium with the rest of the system. These points are sometimes referred to as “triangular Lagrange points” or “Trojan points” and come from the Trojan asteroids at the Sun-Jupiter L4 and L5 points. These asteroids were named after characters from Homer’s Iliad. Asteroids at the L4 point leads Jupiter and is referred to as the “Greek camp” while those are the L5 are referred to as the “Trojan camp”.

The Earth-Sun system, like the Jupiter-Sun system, also uses the same terms of reference. There is one known Greek asteroid in the Earth-Sun system, 2010 TK7, first detected in October 2010 by Dr. Martin Connors using the Wide-field Infrared Survey Explorer (WISE) . The asteroid’s designation come from the provisional naming system for minor planets. This asteroid which has a diameter of about 300 meters oscillates about the L4 Lagrangian point. The region around these points is known to contain interplanetary dust. As people tend to search for asteroids at much greater elongations, very few searches have been done at these locations. Currently, there are no confirmed or suspected L5 Trojans of Earth which makes both Raj’s and Alex’s work interesting and something to talk about.

Further Reading

The Big Bang Theory of Trans-Neptunian objects

Season 02, Episode 04: “The Griffin Equivalency”



Trans-Neptunian Objects in the Solar System



Provisional designation of Minor Planets



First Letter (A-G)

First Letter (H-O)

First Letter (P-V)

First Letter (W-Y)
Nov 16 Dec 1 Dec 16


Second Letter (A-K)
1 2 3 4 5 6 7 8 9 10

Second Letter (L-U)
11 12 13 14 15 16 17 18 19 20

Second Letter (V-Z)
21 22 23 24 25

40 & = 25 + 15 \\
\therefore P & = 15

Planet Bollywood

Q & = 16 \\
25 \times 17 & = 425
And \(425 + 16 = 441\).


Long live Planet Bollywood!

Battery Sized Satellites explore the Universe

Some of the smallest satellites ever launched will soon start unlocking the secrets of the largest starts in our Universe. These satellites, no bigger than a car battery, are designed to observe some of the most luminous stars in the night sky including the massive blue stars that are the precursors to supernova explosions. To do this, astronomers will use these satellites to observe a star’s surface vibrations caused by processes occurring deep inside a star in a similar way a geophysicist uses seismic waves to probe our Earth’s interior. These stars are important as some of them generate the heavy elements needed to give birth to new generations of stars and planets. In fact, our solar system was made from elements produced by earlier generations of similar massive luminous stars.

A BRITE microsatellite

The space telescopes are the size of a car battery. (Credit: UTIAS Space Flight Laboratory)

The BRIght Target Explorer (BRITE) Constellation is a collection of six satellites that operate in pairs. Each pair was designed and made by the three participating nations in this project: Canada, Australia and Poland. They each measure the size of a 20 centimeter cube weighing no more than 8 kilograms, making them about the size and weight of the average car battery. By equipping each satellite with Charged Coupled Devices or CCD cameras with one camera having a red filter and the other a blue one, scientists can not only observe stars with an average temperature of 10,000 Kelvin making these stars among the hottest and brightest in our sky but can also better detect variations in stellar output as well as the reasons behind that variation.

There are some very compelling reasons for launching theses satellites into space rather than build earth based observatories. Atmospheric turbulence, weather, the day-night cycle of our planet perturb ground based observations, making readings less precise. A space based system can avoid all that and while the satellites are small in size, they are a cost-effective solution to astrophysical research.

You can visit the BRITE Constellation page to learn more.