What Apollo 11 Left Behind

The Apollo 11 Lunar Laser Ranging Experiment.

Neil Armstrong and Buzz Aldrin left behind more than just their footprints on the Sea of Tranquility when Apollo 11 returned home. They left behind an experiment that is still running today. Circled by footprints in the Moon dust is an array of 100 mirrors pointing towards Earth, known as the Lunar Laser Ranging Experiment (LLRE). The Apollo 11 astronauts left it there during their final Moon walk. Today, over forty years later, the device still works.
   Using these mirrors, we can bounce laser pulses off the Moon’s surface to measure the Moon’s distance very precisely. This allows us to track the moon’s orbit over time and test theories of gravity.
   Directed by telescope, a laser sends a pulse of photons which hit the array and bounce straight back to where they came from. About 2.5 seconds later, a detector on Earth catches one of the returning photons. This allows us to pinpoint the Moon’s distance with incredible precision, to within a few millimeters. 

A graph showing photons returned from the LLRE. Credit: APOLLO Collaboration.

   It is extremely difficult to catch these reflected photons, which scientists have described as like hitting a moving dime with a rifle bullet from three kilometers away. Yet astronomers at the Apache Point Observatory in New Mexico have been doing just that with their laser ranging system and 3.5 m telescope. 
   By carefully tracing the Moon’s orbit, we have learned that it is moving away from Earth at a rate of 3.8 cm per year (due to our oceanic tides). We have also verified that the universal force of gravity is very stable. Newton’s gravitational constant has changed less than one part in 100 billion since the experiment began. Physicists use the laser results to check general relativity, Einstein’s theory of gravity. Einstein’s equations predict the shape of the Moon’s orbit perfectly.
   The LLRE requires no power source and it hasn’t been covered with dust or destroyed by meteoroids, as feared by Apollo 11 planners. So lunar ranging should continue for decades or even centuries, further increasing our understanding of gravity.

Newton’s Most Famous Equation

Diagram of the torsion balance experiment
performed by Henry Cavendish in 1798.

According to Newton’s law of gravity, every object in the universe attracts every other object, with a gravitational force proportional to the product of their masses and inversely proportional to the square of the distance between them. 


F = G x m1 x m2 / r²


   This equation is one of the most famous in physics, almost as famous as Einstein’s equation relating energy and mass. F is the force between two masses, m1 and m2. The distance between the centers of the two masses is r, and G is Newton’s gravitational constant. Newton’s constant can’t be deduced purely from math. In order to calculate G, the gravitational force between two known masses at some known distance must be measured. Ironically, Newton never knew the value for his own constant. 
   Because gravity is so weak, G was too small to measure until the end of the 18th century. In 1798, the British scientist Henry Cavendish was able to work out the value of this constant in an experiment designed to determine the mass of the Earth. He used a torsion balance: two lead balls attached to the ends of a light, wooden rod suspended by a thin wire. He then brought two larger lead balls next to the smaller ones, so that they would exert a gravitational force and twist the rod a small amount. Cavendish’s experiment was remarkably sensitive for its time. The twisting force exerted in his experiment was roughly equivalent to the weight of a grain of sand. Cavendish was careful to prevent wind and temperature changes from interfering by placing the whole apparatus in wooden box enclosed in a shed. He used a telescope to observe the motion of the rod, which was only 4.1 mm. By using a vernier scale he was able to achieve an accuracy on the order of one hundredth of an inch. It would be nearly a century before someone would produce a more accurate result. 
   In metric units, G is the gravitational force between two one-kilogram masses separated by one meter, about 6.7 x 10^-11 newtons. That is a very small force, considering a newton is about one fifth of a pound. For example, consider how massive an object would have to be in order to exert one newton of force on a one hundred kilogram man at a distance of 10 meters. If you do the math, you will find that the mass, m1 = (F x r²) / (G x m2) = 6.7 billion kilograms, about the same as the mass of the Great Pyramid of Giza. So even if you had an 10-meter-radius sphere made of solid lead, it would not exert a full newton of gravitational force even if you lying on top of it (assuming you don’t weigh more than 100 kg).
   It should be noted, of course, that although Newton’s law of gravity is sufficiently accurate for most practical purposes, Einstein’s theory of general relativity must be employed when the objects being studied are moving at relativistic speeds or if their masses are large and close together. That is why there is a slight discrepancy in the orbit of Mercury when comparing its observed motion with its predicted motion using Newtonian calculations.

The Next Materials Revolution

A model showing graphene’s chicken wire structure.

What started with a few experiments with Scotch tape and a pencil could some day become the next materials revolution as important as the silicon chip or even plastic. 
   In 2004, Konstantin Novoselov was a post-doctorate researcher studying conductivity in the lab run by Andre Geim at the University of Manchester. Creating graphene started as one of their after-hours projects they were doing for fun. Geim and Novoselov were trying to creating a substance that was only one atom thick. They spent a while trying to make the thinnest possible slice of graphite, to see if it would work. Over the next few weeks they made several attempts. At about the same time the lab had received an electron microscope that they could use to see atomic structures. Geim and Novoselov wanted a good structures to look at, and graphite came up as an obvious choice. 
   They discovered that the best way to prepare a smooth surface on the graphite was to take a piece of Scotch tape and use it to peel away any dust or residue. They were throwing away the tape, but then at some point it was suggested that they should take a look at the residue on the tape and see if it would work as a transistor. On the first attempt they were nearly successful and over many months they improved the conductivity of the graphite by making it thinner and thinner. Eventually they were able to produce the two-dimensional material with its characteristic chicken-wire structure. The uniquely symmetrical arrangement of electrons enhanced conductivity and strength, and they announced graphene’s properties in 2004.
   Almost immediately there was a flood of talk of what this material could be used for, creating everything from super-strong aircraft to paper-thin, foldable touch screens. Graphene could replace glass since it is perfectly transparent. Graphene could also be layered with plastic, revolutionizing nanotechnology. Integrating graphene into existing technology will take years. Geim and Novoselov are trying to show how graphene can be used as a conductor instead of silicon as the main material in electronic circuitry, but it may take decades before the technology becomes commercially viable. Graphene will most certainly be used in the creation of lighter, stronger, more flexible materials that will find uses in prosthetics, aerospace design, and mobile phone technology. The possibilities are endless.

Graphene

Anyone want to reproduce a Nobel Prize-winning experiment? The materials list is quite extensive: a pencil and scotch tape. A pencil contains graphite, which consists of sheets of carbon in a hexagonal lattice. When you write on the sticky side of the tape, layers of graphite slide off the tip of the pencil and stick to the tape. 

The atomic structure of graphite. One sheet of graphite,
when isolated, is known as graphene.

   By folded the tape in half, you will cleave the flakes of graphite when you open it back up. If you repeat this procedure a few times you will create increasingly thin layers where some will be only a single atom thick. You have created graphene.
   Graphene is the thinnest material known to man. Not only that, it is the strongest. It conducts electricity as well as copper and it is also the best thermal conductor. 
   In 2004, Konstantin Novaselov and Andre Geim created graphene using this technique known as micromechanical cleavage. Their success was quite unexpected because it was thought a single layer of graphite would not be chemically stable. In 2010, Novaselov and Geim were awarded the Noble Prize in physics for their discovery. Apparently, creating a two-dimensional crystal is a big deal!
   Graphene conducts electrons faster than any other substance at room temperature, 100 times faster than silicon. This is because of the extraordinarily high quality of the graphene lattice where the atoms line up so regularly that there is not a single atom out of place. With no defects in the hexagonal lattice, the electrons do not scatter. They travel so fast that relativity must be used to fully understand how they move. The carbon atoms in the lattice create very strong yet flexible bonds, making graphene bendable and 200 times stronger than steel by weight.
   Welcome to nanotechnology, where very tiny devices are less than 100 nanometers in size. A nanometer is a billionth of a meter (1 nm = 1/1,000,000,000 m). That is roughly the size of 10 atoms. Scientists are exploring graphene’s unique material properties to create thin, mechanically tough, electrically conducting, transparent films. Such films are badly needed in a variety of electronics applications from touch screens to solar cells. We will finish up our discussion of graphene and other possible applications in next week’s column.