Mysteries So Bright

Come unto me, all ye that labor and are heavy laden, and I will give you rest. (Matthew 11:28)

If you have studied the problems of keeping a satellite in orbit around the earth, you know that there have to be periodic adjustments made to its speed and direction. Otherwise the orbit will degrade so that a satellite can no longer perform its function. The adjustments are usually made by commanding small jets to eject a precise amount of compressed gas that is stored on the satellite. The ground controllers call these adjustments “burns.”

And this problem is prevalent no matter where you would try to place a space object in the solar system except at some very special points in space called Lagrangian Points. They are labeled L1, L2, … L5. There are 5 L points for each pair of orbiting bodies, like the Sun-Earth system and the Sun-Mars system as well as for the Earth-Moon pair of bodies, as seen in the diagram that is in the Wikipedia: Lagrangian Point article.

Lagrange points for Earth-Moon

The two points, L4 and L5, are the best choices for a stable location because if the satellite drifts away from the point in any direction, the effects of gravity plus momentum will keep it close to the Lagrangian point. The blue arrows show the limits of the “safe region”.

On the other hand, L1, L2, and L3 only have temporary stability and a satellite at those positions has to have periodic adjustments to keep it there. Drifting any amount toward or away from the earth or moon will produce instability. Thus, though it takes less “fuel” to keep a satellite at those points, the “burns” are still required.

I just chatted on-line with my friend Chandra in India – he worked on a version of this problem in college. It was called the 3-body problem discussed by Newton in 1687 and by Euler in 1767, and then by Lagrange in 1772.( ref: Wikipedia article: Three-body_problem)

For only 2 bodies in space, the prediction of their orbits around each other is easily calculated. But add a 3rd body and their orbits become unpredictable except in restricted circumstances. Outside those restrictions, the motion is chaotic – in fact, the academic field of Chaos was established to deal with this kind of motion.

I find it amazing that our Lord Jesus, who was the one through whom the universe was created (Hebrews 1:2), is also the one that made the laws by which it behaves. He knows all about the chaos that it is all heading for, and provides for us a safe, stable resting place in Him.

Take my yoke upon you and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls.
For my yoke is easy, and my burden is light.
(Matthew 6:29-30)

David and his bridge that underwent destructive testing in high school

The owl will nest there and lay eggs, she will hatch them, and care for her young under the shadow of her wings. (Isaiah 34:15)

Periodically our son and grandson come to search the stuff stored in our attic for toys and memories.  This past visit, they found a balsa-wood model bridge that my son had built in high school for a classroom contest.  I had suggested that the catenary shape might be the strongest shape to use for the weight-bearing parts of the bridge.  I left the rest to him.

During the contest, the bridges were subjected to increasing weight until they broke and dropped the weight.  He recalls that his bridge came in second, but in a way, was the best one because his design used the least amount of  balsa wood – it was light weight but very strong.

What is the catenary shape?  It is the shape of the St. Louis Arch and of many ancient and modern arches used in architecture;  the shape is most easily achieved by hanging a chain by its two ends. The natural shape it takes between the attachment points is the catenary shape.  It is also very close to the shape of the ends of an egg.

While teaching physics, my students showed how strong this shape is.  In a simple demonstration two students held a bed sheet between them to act as a catching net.  A raw egg (the free-roaming chicken, barnyard eggs are best for this) is thrown hard into the sheet by another student, and, unless the sheet is missed, the egg will not break.  At least I never saw it break from hitting the sheet, assuming the catchers did not let it roll off onto the ground.

The other impressive demonstration requires two straight-sided glass cylinders, such as drinking glasses, where one glass will fit closely inside the other.  The egg (raw)  is padded below and above with a sponge or folded paper towels, for example, and placed in the larger glass.

Important!  The egg is placed so the long axis of the egg is parallel to the sides of the glass; in other words, the egg is placed “on end” in the glass. The bottom of the inner glass is then slid into the outer glass until it is resting on top of the padded egg.

Using a chair to steady the person, and standing on a stool about the same height as the nested glasses, he or she gradually places all of his or her weight on the upper glass showing that the egg will support the weight without crushing.  Of course, there is a limit of how much it will support.  When I last did it, I probably weighed about 200 lbs, and did not break the egg.

Isn’t it amazing, that the law of gravity, as established by the creator, is what causes a chain to hang as it does, that this same shape is that of the eggs laid by various birds and reptiles, and that it forms the strongest type of free-standing arch?  Isaiah 34:15 says, “The owl will nest there and lay eggs, she will hatch them, and care for her young under the shadow of her wings.” God loves us and also invites us to abide in His strong shelter.

“It is the glory of God to conceal a matter;  to search out a matter is the glory of kings” (Proverbs 25:2)

In the early days of science,  it was believed that there was no connection between electricity and magnetism.  The magnetic force was found in rocks with iron ore in them, and then magnets were made by rubbing these special rocks against iron or steel.  These were then used to make magnetic compasses, giving a wonderful advancement in navigation.

The early experiments with electricity included the investigation of lightning, made most famous with Benjamin Franklin’s dangerous flying of a kite during a thunderstorm (he and his assistant could have been easily killed by a direct hit).   It was also discovered that heat and light could be produced by passing the current from a battery through a thin wire.

However, to show there was no connection between electricity and magnetism, a magnetic compass was placed beneath a wire through which electric current was passed. The equipment was arranged so that the wire was at right angles to the compass needle, thinking that surely if there were a force between them, the needle would be deflected to become parallel to the wire.  But there was no deflection.

However, in 1820, Hans Oersted at the University of Copenhagen while preparing this demonstration, discovered that if the compass needle and the wire are parallel to start with, that the needle would swing to being perpendicular to the wire – just the opposite of that which had been predicted.  It was a serendipitous moment.  He had shown a connection between electricity and magnetism.

This led to the building of an electric catapult, hence the nickname given this force, which today is called the Lorentz Force, named after Hendrik Lorentz who formulated the mathematical equation in 1892 that describes it.

To picture the catapult, imagine a child’s swing scaled down to fit on top of a table.  You would use thin wires instead of chains to hold up the “seat” which is also made of wire. Everything would be connected to a battery so that electric current will flow down one “chain”, through the “seat”, and back up the other “chain.”

Directly below the “seat” you would hold a bar magnet with the north pole pointing upward. When the current was turned on through the “swing,”  the “seat” would be “catapulted” forward or backward, depending on the direction of the current.

You may have seen toys that swing back and forth tirelessly, run by a single AA battery that is based on this principle.  In fact the electrically powered baby swings operate by this catapult force. More importantly this Lorentz Force is what powers electric motors which have played such a large role in the twentieth and twenty-first centuries.

Proverbs says, “It is the glory of God to conceal a matter;  to search out a matter is the glory of kings” (Proverbs 25:2)  It is such a blessing that He also puts in our hearts and minds the desire to discover these hidden laws of His creation.