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L - Factary


Lagrange Points


The French mathematician Joseph-Louis Lagrange discovered five special locations in the vicinity of two orbiting masses (for example the Earth and Sun) where a third, smaller mass, can orbit at a fixed distance from the larger masses. These so-called Lagrange Points are those positions where the combined gravitational pull of the two large masses precisely balances the centrifugal force felt by the smaller body in its orbit.


The locations of the 5 Lagrange points in the Sun-Earth system are shown in the image below. The first Lagrange Point (L1) is in between the two bodies. The SOHO spacecraft orbits the Sun at a place near the (L1) point of the Earth-Sun system.

Image showing the Lagrange points


L1, L2 & L3 are known as Saddle points L4 & L5 are known as Stable points


(The diagram is not to scale.)



Beware! It is often wrongly stated that the (L1) point is where the gravitational pull of the Sun and the Earth balance. From your knowledge of the mass of the Sun and Earth and how the strength of gravity changes with distance can you show why that statement is wrong?




The force of gravity between two objects of mass M1 and M2 separated by a distance R is:


      G x M1 x M2
F = _____________
     R x R

(where G is the gravitational constant, a number)


Let us place a satellite directly in line between the Earth and Sun and find out where it has to be for the gravity force from the Sun to be equal to the gravity force from the Earth.


If the mass of the satellite is m, the mass of the Sun is Ms and the mass of the Earth Me and the satellite's distance from the Sun is Rs and its distance from the Earth Re, then we want that:


G x Ms x m

Rs x Rs


G x Me x m


Re x Re


The 'G's and 'm's cancel out so we are left with:





=  square root (Ms/Me)


Since we know that the ratio of the masses of the Sun and Earth (Ms/Me) is approximately 333,000 then the ratio of distances to the satellite must be:





=  square root(333000) = 577


Since the Earth-Sun distance is about 150,000,000 km then our satellite must be placed about 259,500 km from Earth (nearer than the Moon) in the direction of the Sun.


This is nowhere near the L1 point which is 1,500,000 km from Earth, so beware of such simple explanations!




Large Angle and Spectrometric Coronagraph. The coronagraph on board SOHO.



LASCO has provided us with some amazing images and movies (Just take a look at our Gallery)




The ancient language from which many modern English words are derived. You've heard of words like spectrum, datum, maximum and minimum? All pure Latin, which is why, if we want to be consistent, their correct plurals are spectra, data, maxima and minima.


LatitudeImage showing the latitudes of the Earth


A north-south coordinate measured on the surface of a sphere. It is the angular distance measured from the centre of the sphere from the equator in the direction of one of the rotational poles. To put it more simply, it's how far north or south you are from the equator, measured in degrees from the centre of the sphere.


Life on Earth


We normally say that all life on Earth depends on the light and heat from the Sun. But there are exceptions - see this note from the Woods Hole Oceanographic Institution in the USA.


"When scientists discovered hydrothermal vents, their initial interest was in the geological and chemical processes taking place on the sea floor. A surprising find was the presence and abundance of life forms in this cold, dark, hostile environment. Here at depths of 2,500 to 3,000 meters, with crushing pressure, scalding and freezing temperatures, toxic chemicals, and absolute darkness, scientists found incredible communities of life. Previously unknown -- and unsuspected -- species of giant worms, crabs, clams, mussels, shrimp, fish, anemones, and other life forms were apparently thriving in these vent communities. Scientists launched a new set of inquiries to understand the biology of these species. Biologists have since learned that bacteria are present at all vent communities and are the base of the food chain here. Instead of using photosynthesis to get their energy from light, these bacteria use chemosynthesis to convert the chemical "soup" of the vent environment. Other life forms either consume the bacteria and thereby get energy directly from their food source, or host them and get energy from the compounds the bacteria produce."


Perhaps even more extreme are the forms of life described in this article by Prof David Wolfek at the University of California.


"Extremophiles, the microorganisms that do not just tolerate, but demand, conditions that would seem to make life impossible, are remarkable for their ability to find nourishment within their barren, rocky habitats. The most basic needs of all life forms are carbon and energy. We obtain these basics from sugars, fats and other organic compounds in the plant- and animal-based foods that we eat. Some extremophiles also live off of dead plants in a way; they utilize ancient buried plant life, often in the form of oil, coal, or other hydrocarbons, as a food source."


"But it turns out that there are other sources of organic carbon buried deep within the Earth that did not originate from the photosynthetic process of plants. Long ago when our planet was first forming, many of the meteors that bombarded the primitive Earth were a type known as carbonaceous chondrites. These contain organic forms of carbon (molecules with both carbon and hydrogen atoms), as well as nitrogen and sometimes traces of water. Although collisions between the Earth and these types of meteorites are rare today, a recent impact occurred near the town of Murchison in Australia, on September 28, 1969. The Murchison meteorite was analysed and found to contain not only organic carbon but several amino acids. Carbonaceous chondrites like the Murchison meteor may have been important in the very origin of subterranean life three and a half billion years ago, in addition to being a source of nourishment for some extremophiles today."


"The most amazing of the extremophiles are the lithotrophs, or 'rock-eaters', which live off of the rock itself. They obtain their carbon from carbon dioxide gas in a process that is similar to photosynthesis in some ways. However, unlike plants, lithotrophs are in the dark, so they must find an alternative to solar energy to power the uptake of carbon (and to power other life functions). It is only recently that we have discovered that the lithotrophs derive their energy by stripping off electrons from the atoms of inorganic minerals in the surrounding rocks or from hydrogen atoms of hydrogen gas in the environment. This is a unique and amazing talent, one that allows lithotrophs to survive completely independent of the Sun, organic food sources and surface life."


Light Year


The distance light (or any electromagnetic radiation) travels in a vacuum in one year (approximately 9.5 million million kilometres). The Moon is about 384,000 kilometres from Earth, so a light beam could travel there and back in about 2.5 seconds or to put it another way, it could go there and back over 12 million times in a year!


Often you’ll hear people say things like, "I remember that happening light years ago". What's wrong with that I hear you shout? If you think about it the whole thing is a bit of an anomaly really. The statement refers to 'time' but a Light Year is actually a measure of 'distance'. However light from distant galaxies does take a long time to reach us, so in some ways we are looking back in time.




See Solar Limb.


Log Tables


Log, or logarithm, tables were used, in the days before electronic calculators, to help speed up calculations with numbers. They used numbers expressed as exponents to a base of 10. In this system

101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
and so on. The small numbers (1,2,3) are called the exponents of the numbers 10,100 and 1000 to base 10.


Q: Can you guess how the number 1,000,000 is written in such a system?
A: 106 ( the exponent is 6 to the base 10 )


Now suppose you want to multiply: 1,000 x 100,000
This could also be written as 103 x 105 and the answer is
100,000,000 or 108
Notice that 3 + 5 = 8, which suggests a quick and easy way to do multiplication.


In other words, we can multiply two numbers by doing an addition of their exponents. Using log tables, it was possible to look up the exponent of any number and so do difficult multiplications and divisions just by adding and subtracting the exponents.


For instance if we need to work out 10.53 x 36.24, we would look up each of the exponents and get 1.0224 and 1.5592, so that


10.53 x 36.24 = 101.0224 x 101.5592


since the sum of the exponents is 2.5816, the answer is 102.5816


But now we need to reverse the process (the tables contained antilogs too!) to find out what number has an exponent of 2.5816. The answer is 381.593. How does that compare with the direct answer from a calculator?


Lockyer, J.Norman (1836-1920)Lockyer, J. Norman (1836-1920)


British solar physicist - famous for discovering helium in the Sun and founding an observatory at Sidmouth in Devon.




An east-west coordinate measured on the surface of a sphere. Unlike latitude, for which the poles and equator form natural reference points, the place at which longitude is zero is just decided by agreement - for example on the Earth it is the longitude of Greenwich in England.


Longitudinal wave


In a longitudinal wave the particle displacement is parallel to the direction of wave propagation.


In this demonstration (by Dr. Dan Russell, Kettering University Applied Physics) you can see the wave travelling through the medium, but if you concentrate on an individual dot in the medium, you’ll see that it doesn’t go anywhere.



Lyot, Bernard Ferdinand (1897-1952)Lyot, Bernard Ferdinand (1897-1952)


French mathematician and physicist who studied light and optics. Famous for inventing the coronagraph, a device for studying the solar corona.


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