Category Archives: Astronomy

Why don’t auroras happen near the equator?


The above picture, taken with the DES satellite on March 13, 1989 during a Great Aurora, shows that some aurora can be seen very far south. The southern edge of this auroral oval extended to the Great Lakes and could be seen almost directly over head. Further south, in Florida, observers saw a bright red glow in the northern horizon, but close to the horizon.

Aurora are commonly seen only at latitudes near 60 degrees, however, a few rare aurora have been seen near the equator, like the 1909 storm seen in Japan. The reason they don’t happen in the equatorial regions is that the flows of energetic electrons and protons that trigger aurora travel along magnetic field lines that connect the distant geomagnetic tail region with the Earth’s surface field. These field lines reach the Earth only in the polar cap areas. In the equatorial zone, the only field lines there connect the two poles via magnetic field lines that are much closer to the Earth and do not each out into the geotail. Some aurora, during exceptional geomagnetic and solar storms, are seen in the equatorial zone, but not very close to the zenith. You still have to look directly north or south to see the auroral glow, so they are still a product of geotail ‘field aligned’ current flows, although over a greatly expanded range of magnetic field lines.

How did the Indigenous Peoples of North America name the Full Moons?


The Harvest Moon goes by many other names. (Credit:Wikipedia). There are several lists of these to be found across the WWW. The Old Farmers Almanac has one such list based upon the Algonquin names. A full Moon name used by one tribe might differ from one used by another tribe for the same time period, or be the same name but represent a different time period. The name itself was often a description relating to a particular activity/event that usually occurred during that time in their location.

Month               ALGONQUIN               OJIBWA
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1. January WOLF MOON GREAT SPIRIT MOON
2. February SNOW MOON SUCKER SPAWNING MOON
3. March SAP MOON MOON OF THE CRUST ON THE SNOW
4. April SEED MOON SAP RUNNING MOON
5. May FLOWER MOON BUDDING MOON
6. June STRAWBERRY MOON STRAWBERRY MOON
7. July BUCK MOON MIDDLE OF THE SUMMER MOON
8. August STURGEON MOON RICE-MAKING MOON
9. September CORN MOON LEAVES TURNING MOON
10. October RAVEN MOON FALLING LEAVES MOON
11. November HUNTER MOON ICE FLOWING MOON
12. December COLD MOON LITTLE SPIRIT MOON

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Colonial Americans adopted some of the Native American full Moon names and applied them to their own calendar system (primarily Julian, and later, Gregorian). For example, the Harvest Moon is associated by the colonists with the full moon nearest the Autumnal Equinox on September 21.

It is also worth pointing out that New Moons also have their own names, though limited in number and refer to the second new moon in a given month. These are called the Secret Moon, Finder’s Moon, Spinner Moon and Black Moon.

Contrary to Creedence Clearwater Revival, there is no such thing as a ‘Bad Moon’.

Here are the dates and times for the next series of named moons for 2017:

Month               ALGONQUIN               
--------------------------------------------------------------------------
1. January               WOLF MOON       January 12,      6:34 am EDT   
2. February              SNOW MOON       February 10,     7:33 pm EDT  
3. March                  SAP MOON       March 12,       10:54 am EDT  
4. April                 SEED MOON       April 11,        2:08 am EDT 
5. May                 FLOWER MOON       May 10,          5:42 pm EST  
6. June            STRAWBERRY MOON       June 9,          9:10 am EST 
7. July                  BUCK MOON       July 9,         12:07 am EST 
8. August            STURGEON MOON       August 7,        2:11 pm EST   
9. September             CORN MOON       September 6,     3:03 am EST   
10. October             RAVEN MOON       October 5,       2:40 pm EDT 
11. November           HUNTER MOON       November 4,      1:23 am EDT  
12. December             COLD MOON       December 3,     10:47 am eDT        
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There is also the famous Blue Moon, which is the second full moon in a given month. The last Blue Moon occurred on May 21, 2016, and the next one will be on January 31, 2018. In four or five years per century, there are two Blue Moons. The first Blue Moon always occurs in January. The second occurs predominantly in March. In the 10,000 years starting with 1600, this is true in 343 out of 400 cases, or 86 per cent of the time. In 37 cases (or 9 per cent), the second Blue Moon is in April. In the remaining 20 cases (5 per cent) it is in May.

In January 1999 we had a Blue Moon in January and one in March. The next event will happen in 2018 also in January and March. Then you will have to wait until 2037 for the Blue Moons in January and March.

Because the events of Halloween Eve are heightened by having a Full Moon in the sky, this Raven Moon on October 31 will next occur in the year 2020.

Why does the moon rise 50 minutes later each day?


Here is a simulation of the moon on nine consecutive nights at the same local time. This image shows the positions of the sun and moon with respect to the stars over a nine-day period. The yellow line is the ecliptic, from which the moon never strays by more than about five degrees. (The sizes of both the sun and moon are exaggerated for emphasis.) Courtesy Daniel Schroder.

Imagine the following line as a part of the Moon’s orbital path across the sky from west to east. The moon travels from West to East across the sky, and makes one full journey with respect to the stars every 27.3 days (a Sidereal Month):

East……………….M……………….West

Now, if it takes 27.3 days to travel once around Earth, the moon must travel 360 degrees/27.3 days = 13.18 degrees/day to the East. This means on the next night, the moon is located 13.18 degrees to the East from last night’s location:

East………….M…………………….West

This means that Earth has to turn an extra 13.18 degrees so that tonight’s moon is in the same sky position as last night’s moon. If last night the moon was just at the eastern horizon, tonight at the same time it is 13.18 degrees below the eastern horizon.

Now, how long does it take Earth to turn 13.18 degrees? Well, in 24 hours, it turns 360 degrees, so in (13.18/360)x 24 = 0.88 hours or 52.7 minutes, the sky rotates the extra 13.18 degrees.

Why do we use the time of the Sidereal month instead of the Synodic month which is 29.53 days? Because we are interested in the moon’s relation to its position relative to the background sky (Sidereal) not whether it is in the same orientation with respect to the Sun and Earth. A Synodic month separates one New Moon from the next New Moon, or any corresponding similar lunar phases on any two cycles. If we were to use the Synodic month, we would get a lunar shift of 12.1 degrees per day, and that the moon would rise 48.7 minutes later each night. The average of the two is 50.7 minutes. The difference between the two is 4 minutes, which is just the amount that the Sun has moved to the East in ITS motion along the sky. This emphasizes that Sidereal time does not depend on the location of the Sun, but Synodic does!

Why are there no ocean tides at the equator?


A typical scene on North Seymour in the Galapagos Islands. (Credit:Wikipedia-David Adam Kess). In general, tides along continental shores near the equator are much less violent than elsewhere.

Tides are a very complex phenomenon. For any particular location, their height and fluctuation in time depends to varying degrees on the location of the Sun and the Moon, and to the details of the shape of the beach, coastline, coastline depth and prevailing ocean currents. Here is a figure that shows the difference between high tide and low tide around the world.

Newton’s explanation is that, when you calculate the difference in gravity between Earth and moon at each point on the surface of Earth, you get the customary graph shown here:

This is also the shape of the ‘equipotential surface’ where mass would be in equilibrium and instantaneously ‘at rest’. There are two gravitational tides: The Body Tide and the Water Tide. The Body Tide is the response of the solid Earth to this gravitational distortion in the solid rock of Earth. The lunar body tide has a height of 0.3 meters relative to the unstressed shape of Earth while the solar body tide is about half this high. The water tides are far higher because water is lower density than rock and is free to flow around Earth’s surface with lower inertia than rock. Water tide heights can exceed 10 meters!

You would think that the solid body tide would flex the ground so severely that pipes, railroad tracks and other systems would flex and break over time. The good news is that the scale of this distortion is continent-spanning as the figure below shows.

So what does this all have to do with whether tides are found at the Equator?

Although Newton gave us the basic gravitational theory for solid body tides, his application of this theory to the behavior of water was not correct in detail. The French mathematician Laplace used Newton’s gravitational theory, but realized that its application to water tides had much more to do with the gravitational forcing of various water oscillations. Water oscillations, treated as a harmonic system with many different resonant frequencies is a much more powerful description of the details of water tides on Earth. When you combine the main lunar water tide and the solar tides acting on a complex shaped layer of water along Earth’s surface, what you get is a very different pattern of high and low water tides shown in this figure.

This figure created by Dr. Richard Ray/Space Geodesy branch, NASA/GSFC, shows the M2 lunar tidal constituent. Amplitude is indicated by color, and the white lines are cotidal differing by 1 hr. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period. Note that this response of ocean water has virtually nothing to do with the simple two-bulges, gravitational stress pattern expected from Newton’s calculation above.

So are there water tides at the Equator? Yes there are, and in fact the only locations that have very weak tides are near the poles!

Could you explain what causes the Moon’s synchronous rotation?


At the top of this article is a figure that shows how deformed the moons shape is from a perfect sphere based on orbital data from the Lunar Orbiter spacecraft. The topography of the Moon referenced to a sphere with a radius of 1737.4 kilometers. Data were obtained from the Lunar Orbiter Laser Altimeter (LOLA) that was flown on the mission Lunar Reconnaissance Orbiter (LRO). The color coded topography is displayed in two Lambert equal area images projected on the near and far side hemispheres.

The tidal force of the Earth’s gravitational field raises solid-body tides on the Moon causing the Moon to be deformed into a non-spherical body resembling a football. The magnitude of this effect is about 20 times the solid-body tide caused by the Moon upon the Earth which is about 20×20 centimeters or 4 meters. When the Moon was first formed, it was closer to the Earth than it is now, so the tidal amplitude was quite a bit greater, moreover, the Moon was molten and so it responded even more strongly to the tidal deformation imposed upon it by the Earth’s gravitational field. As a result, the shape of the Moon is very far from being spherical. The Moon was originally rotating faster than it is now so that 3-4 billion years ago it was not orbiting the Earth as fast as it was rotating about its axis.

Over the years, however, the gravitational tidal forces acting upon the non-spherical body of the Moon have modified its non-spherical shape, and caused a systematic dissipation of the Moon’s rotational energy via friction. It costs a lot of energy to deform the Moon, and this energy is lost through the internal friction of rock rubbing against rock within the Moon to raise the solid body tides. Because the Moon may already have solidified into a football-shaped non-spherical body, there is a portion of the Moon that is always slightly closer to the Earth than other portions of the Moon. This becomes a ‘handle’ that the gravitational field of the Earth can ‘grab onto’ to apply a slightly greater force upon the Moon that at other times during the lunar orbit around the Earth. A similar deformity exists in Mercury which has aided the Sun in synchronizing Mercury into a 2:3 spin-orbit resonance. For the Moon, and the larger satellites of the other planets, a similar deformity leads to a 1:1 resonance so that the same side of the satellite always faces the planet.

So, a combination of the Moon’s initial deformation when it was molten and solidified in the Earth’s tidal gravitational field, together with the on-going tidal deformation, leads to a preferred orientation to the Moon in its orbit which the system relaxes to over billions of years.

Why doesn’t the Sun blow up?


In fact, the Sun is doing a slow-motion explosion. It is shedding about 600 million tons every second in light energy, and it is loosing about 100 trillionth of its mass every year in the so-called solar wind. Here is a satellite photo of one of these mass ejections seen by the NASA/ESA SOHO satellite on December 2, 2003. These are dramatic events and often eject ‘a billion tons’ of plasma every few weeks or months. As impressive as they are, the sun is far more massive by a factor of a billion-billion times (1018).

But the sun will never blow up the way we think of a genuine explosion. It is the wrong kind of star to be either a nova or a supernova. It has no companion star for mass-transfer, and its mass is well below the 6-8 solar-mass limit when supernova detonations start to occur.

The energy of the Sun, the thermonuclear fusion which produces all the heat and light, is occurring in the core of the Sun. The weight of all the mass in the Sun in the overlying layers is so enormous that the Sun is in an equilibrium state where the internal thermal pressure is balanced by the gravitational pressure directed inwards.

Eventually, this balance will cease as the core depletes its hydrogen fuel. The core will collapse and heat up causing the outer layers to expand as a planetary nebula like the one shown here: NGC 6720 (Credit:ESA). This is still not a detonation that shatters the sun into interstellar space. In fact, more than 90% of its mass is left behind as a white dwarf ,which is a stable configuration of matter.

Has the loss of mass by the Sun over the last 4 billion years been enough to affect planetary orbits?


Fron the ISS ,our sun is a dazzling star (Credit: NASA/ISS). The luminosity of the Sun is 200 trillion trillion watts or 2 x 10^33 ergs per second. From Einstein’s famous equation, E = mc^2, and using c = 3 x 10^10 centimeters/sec, the Sun’s luminosity is equal to a loss of mass from the fusion cycle of about 2 x 10^12 grams/second. Over one year this is 7 x 10^19 grams, and over the entire life of the Sun to date is about 3.1 x 10^29 grams. The mass of the Sun is 4 x 10^33 grams so this loss equals 0.008 percent of its current mass. The mass of Jupiter is about 0.1 percent of the Sun’s current mass, so over the Sun’s entire lifetime to date, it has lost barely 0.08 percent of Jupiter’s mass, or about the mass of the Earth.

We can estimate how much this mass loss would have changed the orbit of the Earth by approximating the orbital dynamics as the balance between kinetic and gravitational potential energy or 1/2 mV^2 = GMm/R where m = mass of Earth, and M = mass of Sun. We see that a reduction in the Sun’s mass by a factor of of 0.00008 causes an increase in the Earth-Sun distance if the kinetic energy of the Earth is held constant. This means that over the last 4.5 billion years, we can estimate that the Earth’s orbit has increased by about 0.00008 x 93 million miles or about 7,000 miles; about the Earth’s own diameter!

The Sun also produces a ‘solar wind’ of particles at a rate of about 10^-14 solar masses per year. The NASA illustration shows the general idea of what this wind does as it travels through interplanetary space. In 4 billion years this amounts to about 0.001 percent of the Sun’s mass, which to the level of our approximations is a factor of 8 times smaller that the mass loss from converting some of its mass into light. However, both the solar luminosity and solar wind have not been constant over 4 billion years, with the sun having been fainter long ago, and its wind having been much stronger when it was first born.

The overall effects of these mass loss rates can be significant when dynamicists try to predict the long-term orbits of planets. We know that small changes in any physical parameter in these ‘non-linear’ mathematical theories can produce substantial changes in the locations of planets in their orbits. It would not surprise me if the sun loosing 1 Earth mass over 4 billion years might also have a significant effect in predictions of where planets are in the distant future.

What is the distance from the Sun to the Earth for each month of the year?


We all know that Earth orbits our sun in an elliptical path, which means that for certain times of the year it is closer to the sun than for others. Here is a distorted view of the basic orbit (Credit: Wikipedia), but beware that the scales are all wrong. There is only a 5 million kilometer difference between the longest and shortest lengths of the ellipse!

According to the 1996 US Ephemeris, on the 21st of each month, the distance to the Sun is:

Month...............distance............

January             0.9840       147,200,000
February            0.9888       147,900,000
March               0.9962       149,000,000
April               1.0050       150,300,000
May                 1.0122       151,400,000
June                1.0163       152,000,000
July                1.0161       152,000,000
August              1.0116       151,300,000
September           1.0039       150,200,000
October             0.9954       148,900,000
November            0.9878       147,700,000
December            0.9837       147,200,000

.................................

where the first column gives the distance in Astronomical Units so that 1.0 AU = 149,597,900 kilometers By the way, I have rounded all of the distance numbers to 4 significant figures. If you want a mathematical formula that gives you the distances in AU using these table entries for month number N, it looks like this:

d(N) = 1.0000 + 0.0163 cos [ (2pi/12)*((N-1)/12) + 200*2pi/360]

As you can see from the table, the Earth is farthest from the Sun when the Northern Hemisphere is in the summer season (July 3), and closest in the winter (January 3). If you were living in the Southern Hemisphere, the seasons are reversed so that in the summer, the Sun is closest and in the winter it is farthest.

Why does Venus rotate backwards from the other planets?


The rotation period of Venus cannot be decided through telescopic observations of its surface markings because its featureless thick atmosphere makes this impossible. In the 1960’s, radar pulses were bounced off of Venus while at its closest distance to the Earth, and it was discovered that its rotation period, its day, was 243.09 +/- 0.18 earth days long, but it rotated on its axis in a backwards or retrograde sense from the other planets. The above image was created by NASA’s Magellan spacecraft whos radar imaging technique was able to detect surface feaatures as small as a few kilometers across.

If you were to look down at the plane of the solar system from its ‘north pole’ you would see the planets orbiting the Sun counterclockwise, and rotating on their axis counterclockwise. Except for Venus. Venus would be rotating clockwise as it orbited the Sun counterclockwise. Venus is not alone. The axis of Uranus is inclined so far towards the plane of the solar system that it almost rolls on its side as it orbits the Sun.

What accounts for the extreme inclinations of the rotation axis of Venus and Uranus? For years it was thought that in the case of Venus that Earth was the culprit. It is a curious fact that as Venus rotates three times on its axis in 729.27 days, Earth goes twice around the Sun ( 728.50 days) This has suggested to many astronomers that Earth and Venus are locked into a 3:2 tidal resonance. There are many bodies in the solar system that seem to be locked into various kinds of spin-orbit resonances, especially families of asteroids with the planet Jupiter. Mercury also seems to be gravitationally locked into some kind of resonance with the Sun since its day (58.646 days) and its year ( 87.969 days) are also in the proportion of 3:2.

Forces acting on spinning bodies result in some peculiar acrobatics. For instance, if you take a spinning top and give it a push, it will begin to wobble in a manner called precession. The axis of the Earth makes a 26,000 year wobble with an amplitude of tens of degrees. This is all due to the influence of the Moon’s tidal attraction of the Earth. In the case of Venus, however, the gentle gravitational forces it may receive over billions of years to place it in a 3:2 resonance with the Earth don’t seem to be strong enough to tip the entire planet over to make its rotation retrograde. The best, current, ideas still favor some dramatic event that occurred while Venus (and Uranus for that matter) were being formed. It is known from the cratering evidence we see on a variety of planetary surfaces, that soon after the planets were formed, there were still some might large mini-planets orbiting the Sun. One of these may have collided with the Earth, dredging up material that later solidified into our Moon. The satellites of the outer planets are probably representitives of this ancient population of bodies. Venus may have experienced an encounter with one of these large bodies in which, unlike for Earth, the material didn’t form a separate moon, but was absorbed into the body of Venus. In addition to mass and kinetic energy, this body would also have contributed angular momentum. The result is that the new spin direction and speed for Venus was seriously altered from its initial state, which could have been very Earth-like. Today, the result of that last, ancient collision is Venus with a retrograde rotation.

This theory may also apply to Uranus provided that the collision happened before the 15 satellites themselves were captured or formed. Their orbital planes look very uniform and show no evidence for a dramatic gravitational event such as a collision. It may be, too, that the Uranian collision event dredged up matter and flung it into orbit around Uranus, and out of this were formed the larger, coplanar, moons of Uranus.

This is, clearly, a complicated and not well understood phenomenon. The facts for Venus point towards a collision event to put its axis and rotation in the retrograde sense. The tidal action of the Earth on Venus, acting steadily over billions of years, then established the 3:2 spin-orbit resonance. Every 2 earth years, the exact same portion of the Venerian ( Cytherian) surface faces Earth. Could there be some sub- surface concentration of mass on this portion of Venus that the Earth can grab onto to create the tidal lock?

How long would a trip to Mars take?


Contrary to the ‘point and shoot’ idea, an actual trip to Mars looks very round-a-bout as the figure above shows for a typical ‘minimum cost’ trajectory. This, by the way, is called a Hohman Transfer Orbit, and is the mainstay of interplanetary space travel. All you need to do is give your payload a few km/sec of added speed at Earth to place you into the right elliptical orbit whose aphelion is at the location of mars, and then when you get there you fire your rockets in the opposite direction a second time to reduce your speed by a few km/sec to put you into a mars-capture orbit. You spend your entire flight coasting between the planets with no rockets firing. That’s what makes it a cheap flight in terms of fuel, but an expensive one in terms of flight time. In the end, it is always fuel cost that wins.

The travel time depends on the exact details of the orbit you take between the Earth and Mars. The typical time during Mars’s closest approach to the Earth every 1.6 years is about 260 days. Again, the details depend on the rocket velocity and the closeness of the planets, but 260 days is the number most often estimated, give or take 10 days. Some high-speed transfer orbits could make the trip in as little as 130 days.

That said, chemical rockets are very inefficient for interplanetary travel with specific impulses of about 250 seconds and maximum speeds of 10 km/sec. For some really quick trips ,engineers consider advanced ion propulsion systems with specific impulses of over 5000 seconds and maximum speeds of 100 km/sec and travel times of a month. Nuclear-thermal rockets can do even better with speeds up to 10,000 km/sec. At these speeds, a trip to Mars becomes less than a week!