THE DAILY ASTRONOMER
Monday, April 12, 2021
Exploratorium XXXVIII:  Your Questions

A bit of time has passed since we've answered questions.  So, today, as the article title indicates, we will answer some recent subscriber questions.     Today's questions pertain to the Sun, moon, Arecibo Radio Telescope and the effect of cosmic expansion on the human body.  

Since the Sun is much more massive than the moon, why is its influence over Earth's tides just 44% that of the moon?  -F. Smith
To answer this question, we must distinguish between gravity and differential gravity.   The magnitude of the gravitational force two massive objects exert on each other depends on the masses of both and on their separation distance.   The greater the mass, the stronger the force.  Conversely, the force diminishes rapidly -with the square of the distance- as the bodies move away from each other.   

                   
The above idealized gravitational model illustrates the gravitational force exerted between two "point masses," defined as massive objects without any physical extent: points in space.     In the real world, massive objects encompass a certain region of space.   Consequently,  the magnitude of the gravitational force exerted on a given object by another will vary along the object.  The area on a body closer to the other massive object experiences a greater force than the part farther away.    This variation of gravity across a massive body is known as differential gravity. 

Because distance is an important factor in differential gravity, a nearby massive object tends to exert a greater differential gravitational force than a more distant object, even if the later object is far more massive.     The moon and, to a lesser extent, the Sun, are both responsible for Earth's tides.       Even though the Sun is about 27 million times more massive than the moon, the moon is 400 times closer to Earth than the Sun and so has a greater effect on the tides. 

         

Because distance is so important, the tides will be higher when the moon is at or near perigee (its closest distance) than they are when the moon is at or near apogee, its greatest distance.    In summary, although the Sun is far more massive than the moon, its fart greater distance makes its contribution to the tides less than that of the moon. 

Can we see the point where the Big Bang occurred?
-Donald B.
Yes and no.
First, look in front of you.   Now, look behind you.  Next, look down the street.   Finally, look through a telescope toward, let's say, the Andromeda Galaxy.    The Big Bang happened at all those points.   What you're asking, though, is can astronomers pinpoint a specific point in space in which the Big Bang happened?    The answer to that question is no, because such a point doesn't exist.     According to the prevailing cosmological theory, the Universe formed out of a singular event dubbed the Big Bang.    Everything was created in that event, including energy, matter, space and time.   A complete nothing.  In fact, one cannot even say that "nothing existed before the Big Bang" because the word "before" is temporally relative.      

The Big Bang region is everywhere and also nowhere.  

Because the moon is moving away from Earth, will solar and lunar eclipses ever stop?
We will address this question in two parts:

SOLAR ECLIPSES
The moon is moving away from Earth at a speed of about 4 cm per year, the same rate at which fingernails grow.   Although the moon's distance from Earth won't increase substantially over a human lifetime, the cumulative effect over millions of years will be substantial..
In approximately 600 million years, the moon's distance will have increased enough to make it always appear smaller in the sky than the Sun.   Consequently, no more total solar eclipses will occur.  Instead, Earth will experience only annular solar eclipses: those in which the moon doesn't entirely block the Sun so that a "ring of light" is visible around the darkened moon.

           
Total solar eclipses will stop in about 600 million years. After that time, the moon will appear smaller in the sky than the Sun.  Consequently, when the moon crosses directly in front of the Sun, an annular eclipse will occur.   


LUNAR ECLIPSES
Lunar eclipses occur when the full moon moves into Earth's shadow cone.    This cone extends for approximately 840.000 miles.     By the time the Sun's life cycle ends in more than five billion years, the moon will not have moved even close to the end of this cone: less than half the distances, actually.     Lunar eclipses will continue to happen throughout the remainder of Earth's life. 

The Universe is expanding all the time. Does that mean that I am expanding, too, and not just in the conventional sense?  
-S.S.
The Universal expansion causes distant galaxies to recede from the Milky Way.  Or, more correctly, to appear to recede from the Milky Way.  In fact, all the galaxies are moving away from each other as a consequence of the expansion.        However, this expansion is not observable at smaller scales, such as at the level of the human being, because local forces are far stronger.     The electromagnetic forces within the body easily overpower such expansion.        Even the gravitational attraction between close galaxies, such as the Milky Way and Andromeda, is stronger than the Universal expansion.  Consequently, these galaxies are moving toward each other at 300,000 miles per hour and will collide in 4 - 6 billion years. 

I heard that the Arecibo Radio Telescope collapsed.  Will that affect the Arecibo Radio message to the M13 Globular Cluster?   -C. Davis
We should  first provide some background.
The Arecibo Radio Telescope, located in Puerto Rico, was the largest radio telescope in the world.  However, toward the end of 2020, the receiver platform collapsed into the dish, rendering it inoperable.



In 1974, astronomers beamed a "message" toward M13, a globular cluster in the constellation Hercules.     Consisting of 1,679 bytes of data, this message contains information about humanity, the solar system, our number system, our basic chemical constituents, and even the radio telescope that sent the message.     The astronomers used 1,679 bytes because 1,679 is a semi-prime number, meaning that iit is the product of two prime numbers, in this case 23 and 73.   When those bytes are arranged in 23 columns and 73 rows, the following image appears:



The message is en route to the M13 Globular cluster, which is approximately 25,000 light years away.    At this moment, the beam continues toward its destination.  Despite the passage of almost fifty years since the transmission, it has only traveled 0.18% of the entire distance.    Although the Arecibo Radio Dish is now defunct, the message it sent will continue to move toward M13.    The telescope's destruction will not affect this transmission at all.



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