Daedalus and Icarus:  A son too close to the Sun

The tragic tale of Icarus and Daedalus truly begins with some bull.      

Poseidon, god of the ocean, bestowed a beautiful white bull onto Cretan King Minos with the expectation that Minos would eventually sacrifice the bull back to Poseidon.  Minos was so enamored of white bull, however, that he secretly stowed it away and replaced it with another.    Foolishly believing he could deceive Poseidon, Minos sacrificed the substitute bull, claiming it to have been the original.   Well aware of the attempted ruse,  Poseidon resolved to punish Minos.  Instead of discharging a thunderbolt -his brother Zeus' preferred punishment method-Poseidon cast a devious spell on Minos' wife Pasiphaë that caused her to fall passionately in love with the white bull Minos kept.    The desperate queen approached Daedalus, the king's brilliant artificer, and begged him to devise a cow suit into which she could conceal herself.  Daedalus built such a convincing suit that Pasiphaë was able to find the bull and satiate her lust.  Through this bestial coupling the queen gave birth to Asterius, the Minotaur: half man, half bull.  The horrified king, having cleverly realized the monstrous child was not his own, commanded Daedalus to construct a labyrinth in which to house it.     Daedalus' maze was said to have been so intricately designed as to have been inescapable, unless one knew the secret escape method.   In it the Minotaur lived miserably, feeding itself on animals and other creatures that the king sent into the labyrinth to sustain it.   Grotesquely, once a year, Minos also sent into it fourteen Athenian youths offered to him as a tribute.    Years before Crete and Athens  had waged a fierce war that Crete won decisively.  In order to maintain the peace, Minos required an annual tribute of fourteen young Athenians to be sent to Crete.    One year Theseus, the son of Aegeus, the king of Athens, volunteered to join the tribute.    Athenians had heard disquieting rumors that the tribute victims were offered to a flesh-eating creature.  The bold Theseus was determined to slay it, whatever it was.    When the tributes arrived at Crete, King Minos' daughter, Ariadne, fell instantly in love with Theseus.  She hastened to see Daedalus and asked him to reveal the secret method by which one could flee the labyrinth.   He told her that to escape the maze, a person would have to tie one end of a thread skein to the entrance.  Anyone within the labyrinth could draw the thread out and then follow it back to the opening.    As Theseus and the others were led toward the labyrinth, Ariadne ran up to him and offered to help him escape the maze provided he took her with him when leaving Crete.     He agreed.  She handed him the thread and told him what to do.   Theseus managed to kill the Minotaur while saving the other tributes.  They promptly fled Crete, taking Ariadne with them.  The furious Minos knew at once that the tributes could have only escaped with Daedalus' assistance.    The king imprisoned Daedalus and his son Icarus within the labyrinth.     As Daedalus was so dazzlingly clever, he anticipated the punishment and concealed two blocks of wax on his person before being detained.    While he and his son were trapped inside the maze, Daedalus collected the many bird feathers that had fallen into it over the years.  Using the wax and feathers, he built two sets of wings which he and Icarus used to fly out of the labyrinth.    Before departing, Daedalus cautioned his son not to venture too close to the Sun for it would melt the wax and cause the wings to fall apart.      Alas, the reckless Icarus was so elated at having become airborne, he failed to heed his father's advice.   He flew far too high and the wings disintegrated.  Icarus plunged to his death as his distraught father looked on.

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THE DAILY ASTRONOMER
Wednesday, April 15, 2020

Remote Planetarium 13:   Newton's Weighty Laws

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Mini biography

Isaac Newton (1643-1727)

Considered  by many to have been the world's greatest scientist, Isaac Newton devised three fundamental motion laws, the Universal Law of Gravitation and invented the Calculus (along with Liebniz).   A full account of his life and work would require volumes.     

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Why are we taking a break from astronomy to study physics?  Well, in the real Universe, they are inextricably linked.   One cannot know astronomy without knowing physics, the branch of science devoted to understanding how the cosmos works.   Physics enables us to explain actions as simple as you walking down to the street to a phenomenon as grand as galactic mergers and collisions.       Today, we discuss Newton's three motion laws and, of course, his Universal Law of Gravitation.    It will all lead naturally to the important theorem in all of astronomy.  

NEWTON'S FIRST LAW:  An object remains in a constant state of motion unless acted upon by an external force.   

Regard the following  object:

At this very moment, the Voyager 1 craft is leaving the solar system at the breakneck speed of 35,290 miles per hour!  At a current distance of nearly 13.8 billion miles, Voyager 1 is the most distant human made object from Earth.    Provided it doesn't collide with any other object,  Voyager 1 will continue moving inexorably through outer space for millions or even billions of years.   One might wonder:   what keeps Voyager 1 moving?   The answer is: itself.    After its launch and a few swings around planets, this spacecraft has attained a rapid speed that it can maintain indefinitely as long as no external force is applied to it.  Newton's First Law explains this "perpetual motion" quite nicely.     Voyager 1's environment is outer space, a region that closely approximates a perfect vacuum.    Nothing impedes it, apart from dust particles which won't slow its progress in the slightest.   When we drive on Earth, we have to constantly press on the accelerator to counteract the retarding effects of wind and friction between the road and tires.  (Let's also not forget the little matter of the planet's gravity field which we certainly feel when driving uphill.)  A driven car constantly experiences external forces.   A spacecraft escaping the solar system experiences none, apart from the meager gravitational pull the distant Sun still exerts.

Planetary motion provides another example of Newton's First Law.    If we could snap off the Sun's gravity, the planets would all start moving along a line tangent to their orbits.  They would all continue traveling along this tangent until some other large body ensnared them.    The planets constantly experience the Sun's external force and so are constantly moving along their present orbits.

NEWTON'S SECOND LAW:   Force equals mass times acceleration

Let's talk about a common misconception.  It is believed that one could easily push an orbiting satellite around because, as it is in space, it is "weightless."   The problem is that all material objects are massive.    Mass measures a body's inertia.  The greater the object's mass, the more it resists changes in its motion.    We know on Earth that pebbles move more easily than boulders.   Place those boulders and pebbles in outer space.  One would find that it would be much easier to alter the motion of the latter than the former.   

    

The amount of force one applies to a resting object such as this drop dead gorgeous soccer ball determines its acceleration.    If you apply a strong force, it will travel quite far until Earth's gravity pulls it down.  If you apply a weak force, it will hardly travel at all.   

As another example: try kicking a car!   An automobile is far more massive than a soccer ball.  In order to apply sufficient force to accelerate a vehicle, you need to press on the accelerator.   The harder you press, the greater the force and also the acceleration.  

NEWTON'S THIRD LAW:   Every action has an equal and opposite reaction

A perfect example:

What better way to demonstrate Newton's third law than with a beautiful rocket launch.  By issuing violent expulsions in one direction, the rocket is propelled quickly in the other.    Newton's "action/reaction" law is the fundamental principle on which rocketry is based.      We wouldn't have sent humans to the moon without it.

Whitewater kayaking offers a more Earthbound example.  When the kayaker pushes his/her oar backward, the kayak moves forward.   The swift currents help immensely with the speed, hence the thrill seeker's partiality for white water kayaking.   

NEWTON'S UNIVERSAL LAW OF GRAVITATION:    The magnitude of the force exerted between any two massive objects is proportional to the masses of both and inversely proportional to the square of their separation distance.

Regard two asteroids:

They exert a gravitational force on each other.   That force depends on the asteroids' masses and their separation distances.    If you doubled the mass of one of the asteroids, the gravitational force it exerts on the other is doubled.   However, if you double the distance between them, the magnitude of that force is reduced to one quarter of its original value.   Triple the distance and the force is reduced to one ninth of its initial value.

Theoretically, gravity's range is infinite.    Even the Andromeda Galaxy is tugging on us a bit.  However, as the Andromeda Galaxy is immensely far away, the force is negligible.   Scientists now know however, that Newton's Universal Law of Gravitation is indeed Universal.

That notion brings us naturally to the

 FUNDAMENTAL THEOREM OF ASTROPHYSICS:  the physical laws that govern Earth are applicable throughout the Universe.  

Without the fundamental theorem, astrophysics would never have gotten off the ground. (pause for mood improving laugh.)      We know that a dropped ball on a planet somewhere in the Perseus Supercluster is experiencing the same forces a ball experiences on Earth.   Even though the force might be weaker or stronger depending on the other planet's surface gravity, the physical principles governing that ball's motion will be the same.  

Knowing that physics is Universal will prove very helpful to us as we continue our excursions through the cosmos.    

Tomorrow, right ascensions and starry declinations.

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