32. Satellite laser ranging

Lasers are amazing things. However, when first invented, they were famously derided as “a solution looking for a problem”. The American physicist Theodore Maiman built the first laser in 1960, which is possibly earlier than you realised. This is because for several years nobody knew what to use them for, and there was no visible technology that made use of lasers. Their main use was as a device for science fiction, where authors imagined them being used as weapons.

This changed in the 1970s, when laser barcode scanners were invented. These essentially just use a laser as a narrow-beam source of light, which is scanned across the barcode using a rotating mirror. A light sensor detects the pattern of light and dark reflections from the barcode and circuitry turns that into digital data, which can then be processed by an attached computer, revealing information such as a product catalogue number. This is hardly a ground-breaking application; you can (and in fact manufacturers do) make barcode scanners using normal light sources as well.

The first consumer device to use lasers was the LaserDisc player in 1978, a home video format using technology that was the forerunner of the compact disc audio player released in 1982. These devices use precisely focused lasers to read tiny indentations on a reflective surface, turning them into data (analogue in the case of LaserDiscs, digital for CDs), in a way broadly similar to a barcode reader. However here the indentations are so small that doing the same with a normal light source would be prohibitively difficult. And so lasers finally found a widespread use.

Today lasers are used in so many applications and technologies that it would be difficult to imagine life without them. They are vital to modern optical fibre communications networks; have many uses in industry for cutting, welding, scanning, and manufacturing, including 3D printing; are used in many forms of surgery and cancer treatments; and have dozens of consumer uses from laser pointers to printers to entertainment.

A laser is a device that emits light through a process known as stimulated emission. This occurs when a population of atoms exists in an excited energy state, meaning that the energy of one or more electrons in some of the atoms is not at the usual minimum energy state. In such a case, an electron can drop back down to the minimum energy state, emitting the excess energy as a photon of light; this is known as spontaneous emission. The stimulated emission part occurs when a photon interacts with another excited atom, triggering it to also drop into the minimum energy state and release a photon of the same energy. This stimulated photon is emitted in the same direction and with the same phase as the original photon (meaning the peaks and troughs of the light waves are in synch). As more emission is stimulated, an intense beam of light of a single wavelength, all travelling in the same direction is generated, known as a coherent beam.

Mechanically, this can be produced by using a transparent medium such as a gas or crystal, in a long cylinder shape surrounded by a bright strobe tube to supply the energy to excite the atoms. One end of the cylinder is a mirror, and the other end is a partly reflective mirror which lets some of the beam out. The light that emerges is a laser beam. Because the light is coherent, it doesn’t spread out like normal light, but travels in a tight line, illuminating only a small spot when it hits something. This means a laser beam is capable of travelling far greater distances than a normal light source of the same intensity, while still being bright enough to be observed.

One of the very first applications for lasers was invented in 1961, but was restricted to industry and research for a decade. If you aim a brief laser pulse at something and time how long it takes for the reflection to come back, you can divide by the speed of light to calculate the distance to the object. This is called lidar, a portmanteau of “light” and “radar”, as it’s the same principle applied to light instead of radio waves. Lidar works to a range of several kilometres for detecting normal objects that partially reflect the incident beam.

But we can do a lot better if we construct a special target that reflects back virtually all of the incident beam. This can be done with a retroreflector. A common design is three flat mirrors arranged around a 90° corner, like the corner of a box. The combination of reflection off all three surfaces means that any incoming beam of light will be reflected back exactly towards its source, no matter what angle it comes in at. If you shine a laser at one of these, you can detect the return pulse over a much greater range. This form of lidar is known as laser ranging.

In 1964, NASA launched the Explorer 22 satellite into near-Earth orbit, about 1000 kilometres altitude. Its main mission was to perform science on the Earth’s ionosphere, but it was also equipped with a retroreflector, and was the first object in space to have its distance measured using satellite laser ranging.

In 1976, NASA launched LAGEOS 1, a satellite designed specifically for laser ranging. LAGEOS has no active components, it is simply a brass sphere, coated in aluminium, with 426 retroreflectors embedded in the surface, so that no matter which way the satellite tumbles, dozens of reflectors are always oriented towards Earth.

LAGEOS 1 is in medium-Earth orbit, at an altitude of nearly 6000 km. This orbit is far from any perturbing influences and so is extremely stable, meaning the satellite’s position at any time can be calculated to a small fraction of a millimetre. This makes it a useful reference point for measuring the distances to stations on the Earth’s surface, by aiming lasers at the satellite and timing the reflected signal.

These measurements are so precise that they give the distance from the ground station to the satellite to an uncertainty of less than one millimetre. By using a reference point located away from Earth, this provides a method of checking motions of the Earth caused by weather systems, earthquakes, isostatic rebound (the slow rising of land in the millennia after glacial ice sheets melted), and tectonic drift. For example, geophysical tectonic modelling suggests that the Hawaiian Islands should be drifting northwards at approximately 70 mm per year. Measurement of the position of the Haleakala laser base station in Hawaii using LAGEOS and similar satellites shows this to be the case.

Laser ranging can also be (and is) used to measure the shape of the Earth. More specifically, it’s used to measure the shape of the geoid, which is the shape that corresponds to mean sea level (averaging out tides and weather) all over the Earth. More formally this is defined as the surface where the Earth’s gravitational field strength is identical to that at sea level. In areas of land, this surface is generally under the ground. The geoid is not perfectly spherical due to the uneven distribution of mass in the Earth. We’ve mentioned a few times that the Earth is approximately an ellipsoid due to the rotational force flattening the poles and causing a bulge at the equator. The geoid is almost an ellipsoid, but varies locally by up to approximately ±100 metres.

Besides LAGEOS 1 and 2, there are a handful of other similar retroreflector satellites. And there are also retroreflectors on the moon. Astronauts on NASA’s Apollo 11, 14, and 15 missions set up retroreflector arrays on the moon’s surface, and the unmanned Russian probes Lunakhod 1 and 2 also have retroreflectors.

Since 1969, several lunar laser ranging experiments have been ongoing, making regular measurements of the distance between the Earth stations and the reflectors on the moon. These measurements can also determine the distance to better than one millimetre.

If you measure the distances from either an artificial satellite or the moon to different points on the Earth’s surface, it’s trivial to show that the points don’t lie even approximately on a flat plane, but that they lie on the surface of an approximately spherical body with the radius of the Earth. Finding an explicit statement such as “This demonstrates that the Earth is not flat, but spherical” in a published scientific article is difficult (because that result is neither surprising nor groundbreaking), but the following diagram shows the model that laser ranging scientists use to correct for effects such as atmospheric refraction, to enable them to get their measurements accurate down to a millimetre.

This shows clearly that laser ranging scientists—who have explicit and direct measurements of the shape of the Earth’s surface—assume the Earth is spherical in order to refine their calculations. They’d hardly do that if the Earth were flat.

References:

[1] Degnan, J. J. “Millimeter accuracy satellite laser ranging: a review”. Contributions of Space Geodesy to Geodynamics: Technology, 25, p.133-162, 1993. https://doi.org/10.1029/GD025p0133

[2] Murphy Jr., T. W. “Lunar Laser Ranging: The Millimeter Challenge”. Reports on Progress in Physics, 76(7), p. 076901, 2013. https://doi.org/10.1088/0034-4885/76/7/076901