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Polar Star SP-3787 - History

Polar Star SP-3787 - History


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Polar Star

(SP-3787: dp. 8,835; 1. 353'3"; b. 49'; dr. 23'1"; s. 11 k.;
cpl. 86)

Polar Star (SP-3787) was built in 1918 by the Baltimore Dry Dock and Shipbuilding Co., Baltimore, Md., requieitioned by USSB for use in NOTS as a refrigerated cargo ship 23 October 1918, and commissioned at Baltimore 4 January 1919, Lt. Comdr. Thomas F. Gorman, USNRF, in command.

Polar Star quickly entered NOTS service, and was sent from New York 19 February 1919 with a cargo of supplies for the use of the USSB in Montevideo, Uruguay. After visiting La Plata and Pernambuco she returned via Barbados to the U.S. 29 April 1919.

Polar Star decommissioned 14 May 1919 at New York and was returned to the USSB.


Lockheed P-2 Neptune

The Lockheed P-2 Neptune (designated P2V by the United States Navy prior to September 1962) was a maritime patrol and anti-submarine warfare (ASW) aircraft. It was developed for the US Navy by Lockheed to replace the Lockheed PV-1 Ventura and PV-2 Harpoon, and was replaced in turn by the Lockheed P-3 Orion. Designed as a land-based aircraft, the Neptune never made a carrier landing, but a small number were converted and deployed as carrier-launched, stop-gap nuclear bombers that would have to land on shore or ditch. The type was successful in export, and saw service with several armed forces.

P-2 (P2V) Neptune
SP-2H of VP-56 over the Atlantic.
Role Maritime Patrol and Anti-Submarine Warfare
National origin United States
Manufacturer Lockheed
First flight 17 May 1945
Introduction March 1947
Retired 1984 from military use
Primary users United States Navy
Japan Maritime Self Defense Force
Royal Australian Air Force
Royal Canadian Air Force
Number built 1,177 (total) [1]
Variants Kawasaki P-2J


Contents

Spherical polygons Edit

A spherical polygon is a polygon on the surface of the sphere defined by a number of great-circle arcs, which are the intersection of the surface with planes through the centre of the sphere. Such polygons may have any number of sides. Two planes define a lune, also called a "digon" or bi-angle, the two-sided analogue of the triangle: a familiar example is the curved surface of a segment of an orange. Three planes define a spherical triangle, the principal subject of this article. Four planes define a spherical quadrilateral: such a figure, and higher sided polygons, can always be treated as a number of spherical triangles.

One spherical polygon with interesting properties is the pentagramma mirificum, a spherical 5-sided star polygon with all right angles.

From this point the article will be restricted to spherical triangles, denoted simply as triangles.

Notation Edit

  • Both vertices and angles at the vertices are denoted by the same upper case letters A, B, and C.
  • The angles A, B, C of the triangle are equal to the angles between the planes that intersect the surface of the sphere or, equivalently, the angles between the tangent vectors of the great circle arcs where they meet at the vertices. Angles are in radians. The angles of proper spherical triangles are (by convention) less than π so that π < A + B + C < 3π. (Todhunter, [1] Art.22,32).
  • The sides are denoted by lower-case letters a, b, and c. On the unit sphere their lengths are numerically equal to the radian measure of the angles that the great circle arcs subtend at the centre. The sides of proper spherical triangles are (by convention) less than π so that 0 < a + b + c < 2π. (Todhunter, [1] Art.22,32).
  • The radius of the sphere is taken as unity. For specific practical problems on a sphere of radius R the measured lengths of the sides must be divided by R before using the identities given below. Likewise, after a calculation on the unit sphere the sides a, b, c must be multiplied by R.

Polar triangles Edit

The polar triangle associated with a triangle ABC is defined as follows. Consider the great circle that contains the side BC. This great circle is defined by the intersection of a diametral plane with the surface. Draw the normal to that plane at the centre: it intersects the surface at two points and the point that is on the same side of the plane as A is (conventionally) termed the pole of A and it is denoted by A'. The points B' and C' are defined similarly.

The triangle A'B'C' is the polar triangle corresponding to triangle ABC. A very important theorem (Todhunter, [1] Art.27) proves that the angles and sides of the polar triangle are given by

Therefore, if any identity is proved for the triangle ABC then we can immediately derive a second identity by applying the first identity to the polar triangle by making the above substitutions. This is how the supplemental cosine equations are derived from the cosine equations. Similarly, the identities for a quadrantal triangle can be derived from those for a right-angled triangle. The polar triangle of a polar triangle is the original triangle.

Cosine rules Edit

The cosine rule is the fundamental identity of spherical trigonometry: all other identities, including the sine rule, may be derived from the cosine rule:

These identities generalize the cosine rule of plane trigonometry, to which they are asymptotically equivalent in the limit of small interior angles. (On the unit sphere, if a , b , c → 0 set sin ⁡ a ≈ a and cos ⁡ a ≈ 1 − a 2 / 2 /2> etc. see Spherical law of cosines.)

Sine rules Edit

The spherical law of sines is given by the formula

These identities approximate the sine rule of plane trigonometry when the sides are much smaller than the radius of the sphere.

Derivation of the cosine rule Edit

The spherical cosine formulae were originally proved by elementary geometry and the planar cosine rule (Todhunter, [1] Art.37). He also gives a derivation using simple coordinate geometry and the planar cosine rule (Art.60). The approach outlined here uses simpler vector methods. (These methods are also discussed at Spherical law of cosines.)

Consider three unit vectors OA, OB and OC drawn from the origin to the vertices of the triangle (on the unit sphere). The arc BC subtends an angle of magnitude a at the centre and therefore OB·OC=cos a. Introduce a Cartesian basis with OA along the z-axis and OB in the xz-plane making an angle c with the z-axis. The vector OC projects to ON in the xy-plane and the angle between ON and the x-axis is A. Therefore, the three vectors have components:

The scalar product OB·OC in terms of the components is

Equating the two expressions for the scalar product gives

cos ⁡ a = cos ⁡ b cos ⁡ c + sin ⁡ b sin ⁡ c cos ⁡ A .

This equation can be re-arranged to give explicit expressions for the angle in terms of the sides:

The other cosine rules are obtained by cyclic permutations.

Derivation of the sine rule Edit

Since the right hand side is invariant under a cyclic permutation of a , b , c the spherical sine rule follows immediately.

Alternative derivations Edit

There are many ways of deriving the fundamental cosine and sine rules and the other rules developed in the following sections. For example, Todhunter [1] gives two proofs of the cosine rule (Articles 37 and 60) and two proofs of the sine rule (Articles 40 and 42). The page on Spherical law of cosines gives four different proofs of the cosine rule. Text books on geodesy (such as Clarke [2] ) and spherical astronomy (such as Smart [3] ) give different proofs and the online resources of MathWorld provide yet more. [4] There are even more exotic derivations, such as that of Banerjee [5] who derives the formulae using the linear algebra of projection matrices and also quotes methods in differential geometry and the group theory of rotations.

The derivation of the cosine rule presented above has the merits of simplicity and directness and the derivation of the sine rule emphasises the fact that no separate proof is required other than the cosine rule. However, the above geometry may be used to give an independent proof of the sine rule. The scalar triple product, OA·(OB×OC) evaluates to sin ⁡ b sin ⁡ c sin ⁡ A in the basis shown. Similarly, in a basis oriented with the z-axis along OB, the triple product OB·(OC×OA) evaluates to sin ⁡ c sin ⁡ a sin ⁡ B . Therefore, the invariance of the triple product under cyclic permutations gives sin ⁡ b sin ⁡ A = sin ⁡ a sin ⁡ B which is the first of the sine rules. See curved variations of the Law of Sines to see details of this derivation.

Supplemental cosine rules Edit

Applying the cosine rules to the polar triangle gives (Todhunter, [1] Art.47), i.e. replacing A by π–a, a by π–A etc.,

Cotangent four-part formulae Edit

The six parts of a triangle may be written in cyclic order as (aCbAcB). The cotangent, or four-part, formulae relate two sides and two angles forming four consecutive parts around the triangle, for example (aCbA) or (BaCb). In such a set there are inner and outer parts: for example in the set (BaCb) the inner angle is C, the inner side is a, the outer angle is B, the outer side is b. The cotangent rule may be written as (Todhunter, [1] Art.44)

and the six possible equations are (with the relevant set shown at right):

To prove the first formula start from the first cosine rule and on the right-hand side substitute for cos ⁡ c from the third cosine rule:

cos ⁡ a = cos ⁡ b cos ⁡ c + sin ⁡ b sin ⁡ c cos ⁡ A = cos ⁡ b ( cos ⁡ a cos ⁡ b + sin ⁡ a sin ⁡ b cos ⁡ C ) + sin ⁡ b sin ⁡ C sin ⁡ a cot ⁡ A cos ⁡ a sin 2 ⁡ b = cos ⁡ b sin ⁡ a sin ⁡ b cos ⁡ C + sin ⁡ b sin ⁡ C sin ⁡ a cot ⁡ A . cos a&=cos bcos c+sin bsin ccos A&=cos b (cos acos b+sin asin bcos C)+sin bsin Csin acot Acos asin ^<2>b&=cos bsin asin bcos C+sin bsin Csin acot A.end>>

Half-angle and half-side formulae Edit

Another twelve identities follow by cyclic permutation.

The proof (Todhunter, [1] Art.49) of the first formula starts from the identity 2sin 2 (A/2) = 1–cosA, using the cosine rule to express A in terms of the sides and replacing the sum of two cosines by a product. (See sum-to-product identities.) The second formula starts from the identity 2cos 2 (A/2) = 1+cosA, the third is a quotient and the remainder follow by applying the results to the polar triangle.

Delambre (or Gauss) analogies Edit

Another eight identities follow by cyclic permutation.

Proved by expanding the numerators and using the half angle formulae. (Todhunter, [1] Art.54 and Delambre [6] )

Napier's analogies Edit

Another eight identities follow by cyclic permutation.

These identities follow by division of the Delambre formulae. (Todhunter, [1] Art.52)

Napier's rules for right spherical triangles Edit

When one of the angles, say C, of a spherical triangle is equal to π/2 the various identities given above are considerably simplified. There are ten identities relating three elements chosen from the set a, b, c, A, B.

Napier [7] provided an elegant mnemonic aid for the ten independent equations: the mnemonic is called Napier's circle or Napier's pentagon (when the circle in the above figure, right, is replaced by a pentagon).

First, write the six parts of the triangle (three vertex angles, three arc angles for the sides) in the order they occur around any circuit of the triangle: for the triangle shown above left, going clockwise starting with a gives aCbAcB. Next replace the parts that are not adjacent to C (that is A, c, B) by their complements and then delete the angle C from the list. The remaining parts can then be drawn as five ordered, equal slices of a pentagram, or circle, as shown in the above figure (right). For any choice of three contiguous parts, one (the middle part) will be adjacent to two parts and opposite the other two parts. The ten Napier's Rules are given by

  • sine of the middle part = the product of the tangents of the adjacent parts
  • sine of the middle part = the product of the cosines of the opposite parts

For an example, starting with the sector containing a we have:

sin ⁡ a = tan ⁡ ( π / 2 − B ) tan ⁡ b = cos ⁡ ( π / 2 − c ) cos ⁡ ( π / 2 − A ) = cot ⁡ B tan ⁡ b = sin ⁡ c sin ⁡ A . B), an b=cos(pi /2<->c),cos(pi /2<->A)=cot B, an b=sin c,sin A.>

The full set of rules for the right spherical triangle is (Todhunter, [1] Art.62)

Napier's rules for quadrantal triangles Edit

A quadrantal spherical triangle is defined to be a spherical triangle in which one of the sides subtends an angle of π/2 radians at the centre of the sphere: on the unit sphere the side has length π/2. In the case that the side c has length π/2 on the unit sphere the equations governing the remaining sides and angles may be obtained by applying the rules for the right spherical triangle of the previous section to the polar triangle A'B'C' with sides a',b',c' such that A' = πa, a' = πA etc. The results are:

Five-part rules Edit

Substituting the second cosine rule into the first and simplifying gives:

Cancelling the factor of sin ⁡ c gives

cos ⁡ a sin ⁡ c = sin ⁡ a cos ⁡ c cos ⁡ B + sin ⁡ b cos ⁡ A

Similar substitutions in the other cosine and supplementary cosine formulae give a large variety of 5-part rules. They are rarely used.

Oblique triangles Edit

The solution of triangles is the principal purpose of spherical trigonometry: given three, four or five elements of the triangle, determine the others. The case of five given elements is trivial, requiring only a single application of the sine rule. For four given elements there is one non-trivial case, which is discussed below. For three given elements there are six cases: three sides, two sides and an included or opposite angle, two angles and an included or opposite side, or three angles. (The last case has no analogue in planar trigonometry.) No single method solves all cases. The figure below shows the seven non-trivial cases: in each case the given sides are marked with a cross-bar and the given angles with an arc. (The given elements are also listed below the triangle). In the summary notation here such as ASA, A refers to a given angle and S refers to a given side, and the sequence of A's and S's in the notation refers to the corresponding sequence in the triangle.

  • Case 1: three sides given (SSS). The cosine rule may be used to give the angles A, B, and C but, to avoid ambiguities, the half angle formulae are preferred.
  • Case 2: two sides and an included angle given (SAS). The cosine rule gives a and then we are back to Case 1.
  • Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and then we have Case 7. There are either one or two solutions.
  • Case 4: two angles and an included side given (ASA). The four-part cotangent formulae for sets (cBaC) and (BaCb) give c and b, then A follows from the sine rule.
  • Case 5: two angles and an opposite side given (AAS). The sine rule gives b and then we have Case 7 (rotated). There are either one or two solutions.
  • Case 6: three angles given (AAA). The supplemental cosine rule may be used to give the sides a, b, and c but, to avoid ambiguities, the half-side formulae are preferred.
  • Case 7: two angles and two opposite sides given (SSAA). Use Napier's analogies for a and A or, use Case 3 (SSA) or case 5 (AAS).

The solution methods listed here are not the only possible choices: many others are possible. In general it is better to choose methods that avoid taking an inverse sine because of the possible ambiguity between an angle and its supplement. The use of half-angle formulae is often advisable because half-angles will be less than π/2 and therefore free from ambiguity. There is a full discussion in Todhunter. The article Solution of triangles#Solving spherical triangles presents variants on these methods with a slightly different notation.

There is a full discussion of the solution of oblique triangles in Todhunter. [1] : Chap. VI See also the discussion in Ross. [8]

Solution by right-angled triangles Edit

Another approach is to split the triangle into two right-angled triangles. For example, take the Case 3 example where b, c, B are given. Construct the great circle from A that is normal to the side BC at the point D. Use Napier's rules to solve the triangle ABD: use c and B to find the sides AD, BD and the angle BAD. Then use Napier's rules to solve the triangle ACD: that is use AD and b to find the side DC and the angles C and DAC. The angle A and side a follow by addition.

Numerical considerations Edit

Not all of the rules obtained are numerically robust in extreme examples, for example when an angle approaches zero or π. Problems and solutions may have to be examined carefully, particularly when writing code to solve an arbitrary triangle.

Consider an N-sided spherical polygon and let An denote the n-th interior angle. The area of such a polygon is given by (Todhunter, [1] Art.99)

For the case of triangle this reduces to

where E is the amount by which the sum of the angles exceeds π radians. The quantity E is called the spherical excess of the triangle. This theorem is named after its author, Albert Girard. [9] An earlier proof was derived, but not published, by the English mathematician Thomas Harriot. On a sphere of radius R both of the above area expressions are multiplied by R 2 . The definition of the excess is independent of the radius of the sphere.

The converse result may be written as

Since the area of a triangle cannot be negative the spherical excess is always positive. It is not necessarily small, because the sum of the angles may attain 5π (3π for proper angles). For example, an octant of a sphere is a spherical triangle with three right angles, so that the excess is π/2. In practical applications it is often small: for example the triangles of geodetic survey typically have a spherical excess much less than 1' of arc. (Rapp [10] Clarke, [11] Legendre's theorem on spherical triangles). On the Earth the excess of an equilateral triangle with sides 21.3 km (and area 393 km 2 ) is approximately 1 arc second.

There are many formulae for the excess. For example, Todhunter, [1] (Art.101—103) gives ten examples including that of L'Huilier:

From latitude and longitude Edit

An example for a spherical quadrangle bounded by a segment of a great circle, two meridians, and the equator is

The area of a polygon can be calculated from individual quadrangles of the above type, from individual triangle bounded by a segment of the polygon and two meridians, [12] or by a line integral with Green's theorem. [13] The other algorithms can still be used with the side lengths calculated using a great-circle distance formula.


Lincoln Ellsworth’s Polar Star

It all started with a penguin. In 1913, Lincoln Ellsworth, the son of a wealthy Chicago businessman, was in London, taking a course in geographical surveying at the Royal Geographic Society. Each week he visited the London Zoo to watch the emperor penguin that Ernest Shackleton had brought back from the Antarctic in 1909. “I used to watch the strange dignified bird for hours,” Ellsworth would later write. “Had it not been for that beautiful emperor penguin…I should probably never have chosen the polar regions as my field of endeavor.”

Ellsworth, an indifferent student, had left New York’s Columbia University 10 years earlier, and had spent the last several years conducting exploratory surveys for railroads and timber companies in Canada and the Yucatan. But after attending the memorial of Antarctic explorer Captain Robert Scott—and spending quality time with the penguin—Ellsworth was determined to become a polar explorer. He was 33 years old and finally had a purpose in life.

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This story is a selection from the January issue of Air & Space magazine

As early as 1914 Ellsworth championed the use of the airplane in polar exploration, meeting with Admiral Robert Peary to promote his idea. In order to become a pilot, Ellsworth entered the Curtiss Flying School in Norfolk, Virginia, but dropped out after a few days. He traveled to Paris, hoping to join the Lafayette Escadrille, but was rejected for being 14 years above the age limit he was grudgingly admitted into the French air force as an observer. He trained in a Caudron biplane Ellsworth spoke no French and the pilots spoke no English, so the training was non-verbal: “A poke in the back meant one thing,” he later wrote, “a rap on the head another.” He should have been sent to an observers’ training camp, but none were nearby, so Ellsworth continued to fly for three months, the only piloting he would ever do. He spent the rest of the war flying a desk.

But something good came out of Ellsworth’s time in Paris: he met Roald Amundsen, discoverer of the South Pole. In 1925, the two men, along with four other team members, attempted to fly from Norway to the North Pole in two Dornier Do J Wal flying boats. (Ellsworth’s father contributed $85,000 to the expedition.) Engine trouble forced them down 120 miles short of the pole. After 25 days on the ice, the crew flew their surviving flying boat to the coast of Spitzbergen, Norway, where they were rescued by a passing seal hunting ship.

The following year Ellsworth and Amundsen, along with 14 crew members and a dog, flew an airship—the Norge—over the North Pole, before landing in Alaska three days later.

Lincoln Ellsworth gave the Polar Star to the Smithsonian in 1936 the year before, he flew it to within six miles of the South Pole. (Eric Long/NASM) The aircraft was one of two Northrop Gammas produced in 1933. The forward cockpit held most of the flight and directional instruments the aft cockpit featured a chart table and navigational instruments, an airspeed indicator, and an altimeter. (Eric Long/NASM)

After these adventures, Ellsworth considered his days as a polar explorer over. But inactivity didn’t suit him, and as airplanes became more dependable, Ellsworth decided to mount his own expedition, this time to Antarctica.

Antarctica, with an area the size of North America, was virtually unmapped. What better way to survey the huge landmass than by air?

Ellsworth needed an airplane sturdy enough to survive buffeting winds. High winds had tossed one of Admiral Byrd’s airplanes half a mile from its lashings, so he chose the all-metal Northrop Gamma, which had a low wing. It had wide skis that could be swapped with wheels or pontoons and, Ellsworth claimed, a cruising range of 5,000 miles. He named the airplane Polar Star and had it shipped from the United States to his base in Norway, where it was placed in the hold of the Wyatt Earp, a herring boat, along with two years’ worth of supplies.

Ellsworth had thoroughly examined the diaries of past Antarctic explorers, who had traveled by dogsled. He believed there were plenty of good landing fields for his aircraft, so he could make his trans-Antarctic flight in several passes if he encountered bad weather, he could land and wait it out.

The Wyatt Earp arrived in the Bay of Whales on January 9, 1934 Ellsworth and pilot Bernt Balchen went aloft for a 30-minute trial flight. But that evening the Polar Star was caught in the ice and crushed Ellsworth had to abandon his attempt and send the aircraft back to the United States for repairs.

In September 1934 the crew tried again, but during a three-month stay, the weather allowed less than 12 hours of flying time, leading a friend of Ellsworth’s to exclaim, “Your Polar Star has traveled farther and flown less than any other plane!”

On the ice in Antarctica: Except for a slightly crumpled fuselage, the Polar Star didn’t experience any difficulty in takeoff or landing. (NASM (a-34223))

In late 1935, Ellsworth made a third attempt, this time with a new pilot, Herbert Hollick-Kenyon, who was more willing to fly in iffy weather. On November 22, after 14 hours in the air, they made their first landing, crumpling the Polar Star’s fuselage in the process. Their radio was also broken and in a final stroke of bad luck, the pair learned that their sextant readings had been incorrect and they were more than 200 miles off course.

Despite the fuselage damage, the Polar Star was able to fly, and the next day the two men took off. In only 30 minutes, low visibility forced them to land. After waiting several days for good weather, they took off again, hoping to find Little America, the camp Admiral Byrd had established in 1928, but after traveling only 90 miles, bad weather forced them to land again, and they had to wait out an eight-day blizzard. After the weather cleared, Ellsworth and Hollick-Kenyon had to dig out the Polar Star using the only item at hand: a teacup. After two more flights, the Polar Star’s fuel was exhausted. Ellsworth and Hollick-Kenyon walked the rest of the way to Little America, where they gorged on supplies left behind by Byrd. Every day for one month, Ellsworth hiked six miles to a meeting point he and the Wyatt Earp’s captain had pre-arranged, finally making contact with the ship.

Ellsworth received a special gold medal from Congress for his discovery of two mountain ranges and for claiming, on behalf of the United States, 350,000 square miles of Antarctic territory.

As for the Polar Star, it was rescued, then loaded onto the Wyatt Earp, which chugged up the coast of South America, through the Panama Canal, and on to New York. In April 1936, when Ellsworth saw the Polar Star lashed to the deck of the fishing boat, he wrote, “She was as good as new but far too dear a relic in my eyes to be permitted to grow old and go to aviation’s boneyard. So I presented her to the Smithsonian Institution.”

The Polar Star is currently on display in the Golden Age of Flight gallery in the Museum on the Mall.


Polar Star SP-3787 - History

From the moment your party steps on-board one of our beautifully refurbished train cars, they’ll feel like they’ve been transported to a simpler, more leisurely time where the distractions and of our modern world suddenly disappear. Breathe deep, enjoy a drink and relax as you lose yourself on a round-trip, four-hour, 25-mile rail journey through the Piney Woods of East Texas where history is just part of the journey.

Vintage steam and diesel locomotives take passengers across the celebrated rails of the Piney Woods Route between the quaint East Texas towns of Palestine and Rusk on a 50-mile roundtrip adventure.

As if our daily trips through Piney Woods weren’t fun enough, our special events really make for an experience your friends and family won’t soon forget. In fact, our events sell out regularly and many of our guests are return visitors from all over the world. After you experience Texas State Railroad first hand you’ll wonder why you ever settled for a chocolate, wine or a beer festival on solid ground! Don’t miss out on the fun, check out our events page today!

Because of special, incidental or consequential situations that may be out of our control, Texas State Railroad reserves the right to adjust our operation between the date of your booking and the day of departure. These changes could include (but not be limited to): locomotive power for the day, passenger car assignments, layover and/or meal time during the four-hour ride and departure and/or arrival times. Thanking you in advance for your consideration.


The Milankovich Theory

The big questions are, of course, what causes such giant glaciers, and will it happen again? Actually, no one is yet completely sure. But an intriguing idea, due to work in the 1930s by the Serbian astronomer Milutin Milankovich, may link them to the precession which Hipparchus discovered.

As already noted, the Earth's orbit is not perfectly round, but is slightly elongated. The Earth therefore comes closest to the Sun in the first week of January (the exact day varies a little). It means that just when the northern hemisphere experiences winter and receives the least amount of sunlight, the Earth as a whole receives the most (the swing is about 3%, peak to peak). This makes northern winters milder, and northern summers are milder too, since they occur when the Earth is most distant from the Sun.

The opposite is true south of the equator: the beginning of January occurs there in summer, and therefore one expects southern summers to be hotter, and southern winters colder, than those north of the equator. This effect is however greatly weakened, because by far most of the the southern hemisphere is covered by ocean, and the water tempers and moderates the climate.

Right now, northern winter occurs in the part of the Earth's orbit where the north end of the axis points away from the Sun. However, since the axis moves around a cone, 13,000 years from now, in this part of the orbit, it will point towards the Sun, putting it in mid-summer just when the Earth is closest to the Sun.

At that time one expects northern climate to be more extreme, and the oceans then have a much smaller effect, since the proportion of land in the northern hemisphere is much larger. Milankovich argued that because winters were colder, more snow fell, feeding the giant glaciers. Furthermore, he said, since snow was white, it reflected sunlight, and with more severe winters, the snow-covered land warmed up less effectively once winter had ended. Climate is maintained by a delicate balance between opposing factors, and Milankovich argued that this effect alone was enough to upset that balance and cause ice ages.

Milankovich was aware that this was just one of several factors, since it turns out that ice ages do not recur every 26,000 year, nor do they seem common in other geological epochs. The eccentricity of the Earth's orbit, which determines the closest approach to the Sun, also changes periodically, as does the inclination of the Earth's axis to the ecliptic. But overall the notion that ice ages may be linked to the motion of the Earth through space may be currently our best guess concerning the causes of ice ages.

Postscript, 28 July 1999. The magnitude of the "Milankovich effect" depends on the difference between largest and smallest distances from the Sun. That, in its turn, depends on the eccentricity of the Earth's orbit, which varies with a 100,000-year cycle, on which a 413,000-year cycle is superposed. J. Rial (Univ. of North Carolina) found signatures of those cycles in the oxygen isotope content of deep-sea sediments, in full agreement with the Milankovich theory. His work is in " Science ," vol. 285, p. 564, 23 July 1999 a non-technical explanation "Why the Ice Ages Don't Keep Time " is on pages 503-504 of the same issue.

Further note: The sea-bottom results have now been compared to hydrogen isotope ratios in deep boreholes in the ice sheets of Antarctica, which took nearly a million years to accumulate ( Science , 11 June 2004, p. 1609). Deep-sea sediments show that in the last million years, but not before, the variation is dominated by a periodicity around 100,000 years. Its origin, the article states, "is one of the unanswered, yet fundamental questions." Ice cores could help explain it.

Exploring Further:

Because of the precession of the equinoxes, the position among the stars of the celestial pole--the pivot around which the celestial sphere seems to rotate--traces a circle every 26,000 years of so. The celestial pole is now quite close to the pole star Polaris, but it will not be so in the future, and wasn't in the past. The ancient Egyptians regarded as pole star the star Thuban or "Alpha Draconis," the brightest star (=alpha) in the constellation Draco, the serpent. For more information about the motion of the pole, see here and here.

A review article, primarily for scientists: Trends, Rhythms and Aberrations in Global Climate 65 Ma to the Present (Ma is million years), by James Zachos, Mark Pagani, Lisa Sloan, Ellen Thomas and Katharina Billups, "Science" vol 292, p. 686, 27 April 2001. Goes beyond variations due to the precession of the equinoxes and also includes variations of orbit eccentricity, inclination between spin axis and the ecliptic and in the precession cycle itself.

The periodicities that enter the Milankovich theory here. Also, look up "Milankovich" in Wikipedia.


History Timeline

Company renamed Polaris Industries Inc. and first snowmobile built in 1955.

Textron, Inc. purchases Polaris; keeps manufacturing operations in Roseau, MN.

TX-L340 uses first Polaris liquid-cooled engine, first independent suspension snowmobile soon follows.

W. Hall Wendel, Jr., named president of Polaris, led management group that purchased Polaris from Textron in 1981.

Polaris achieves $1 billion in sales for first time.

Victory Motorcycles debut, with Indy Car driver Al Unser, Jr. riding the first bike into Planet Hollywood restaurant at the Mall of America. Polaris expands its off-road business with the Polaris RANGER side by side vehicle.


Dismissing and Summoning Spirits

In your Collection, you can dismiss Primary and Support Spirits to obtain their cores. Primary Spirits provide their type’s core (Attack, Shield, Grab, Neutral). All Support Spirits provide Support Cores when dismissed. You also gain Spirit Points (SP) when dismissing Spirits. The amount of SP you gain is determined by the Spirit’s Rank. Primary Spirits also provide more SP with higher levels.

  • Favorite Spirit: By pressing (ZL) you can favorite Primary and Support Spirits. This allows them to be sorted as such and prevents them from being dismissed accidentally. If you want to dismiss a favorited Spirit simply un-favorite it first, (ZL).

Polar bear

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Polar bear, (Ursus maritimus), also called white bear, sea bear, or ice bear, great white northern bear (family Ursidae) found throughout the Arctic region. The polar bear travels long distances over vast desolate expanses, generally on drifting oceanic ice floes, searching for seals, its primary prey. Except for one subspecies of grizzly bear, the polar bear is the largest and most powerful carnivore on land. It has no natural predators and knows no fear of humans, making it an extremely dangerous animal.

What is a polar bear?

A polar bear is a great white northern bear (family Ursidae) found throughout the Arctic region. Except for one subspecies of grizzly bear, the polar bear is the largest and most powerful carnivore on land. It has no natural predators and knows no fear of humans, making it an extremely dangerous animal.

What do polar bears eat?

Polar bears are mostly carnivorous. They eat the ringed seal as well as the bearded seal and other pinnipeds. Additionally, polar bears are opportunistic as well as predatory: they will consume dead fish and carcasses of stranded whales and eat garbage near human settlements.

What are some examples of polar bear adaptations?

One important adaptation of polar bears to their unique climate is the transparency of their thick fur, which allows sunlight to pass through and reach their black skin, where heat from the sun is then absorbed. Another adaptation is polar bears’ use of only their front limbs when swimming, which is found in no other four-legged mammal.

Are polar bears an endangered species?

No, polar bears are not an endangered species, but they are threatened. In 2015 the International Union for Conservation of Nature (IUCN) Polar Bear Specialist Group designated polar bears as a vulnerable species. According to the IUCN Red List of Threatened Species, the category of vulnerable, as distinct from the category of endangered, means that polar bears have a slightly lower risk of extinction than if they were endangered.

Polar bears are stocky, with a long neck, relatively small head, short, rounded ears, and a short tail. The male, which is much larger than the female, weighs 410 to 720 kg (900 to 1,600 pounds). It grows to about 1.6 metres (5.3 feet) tall at the shoulder and 2.2–2.5 metres in length. The tail is 7–12 cm (3–5 inches) long. Sunlight can pass through the thick fur, its heat being absorbed by the bear’s black skin. Under the skin is a layer of insulating fat. The broad feet have hairy soles to protect and insulate as well as to facilitate movement across ice, as does the uneven skin on the soles of the feet, which helps to prevent slipping. Strong, sharp claws are also important for gaining traction, for digging through ice, and for killing prey.

Polar bears are solitary and overwhelmingly carnivorous, feeding especially on the ringed seal but also on the bearded seal and other pinnipeds. The bear stalks seals resting on the ice, ambushes them near breathing holes, and digs young seals from snow shelters where they are born. Polar bears prefer ice that is subject to periodic fracturing by wind and sea currents, because these fractures offer seals access to both air and water. As their prey is aquatic, polar bears are excellent swimmers, and they are even known to kill beluga whales. In swimming, the polar bear uses only its front limbs, an aquatic adaptation found in no other four-legged mammal. Polar bears are opportunistic as well as predatory: they will consume dead fish and carcasses of stranded whales and eat garbage near human settlements.

Mating occurs in spring, and implantation of the fertilized ovum is delayed. Including the delay, gestation may last 195–265 days, and one to four cubs, usually two, are born during the winter in a den of ice or snow. Cubs weigh less than 1 kg at birth and are not weaned until after they are two years old. Young polar bears may die of starvation or may be killed by adult males, and for this reason female polar bears are extremely defensive of their young when adult males are present. Young remain with their mothers until they reach sexual maturity. Females first reproduce at four to eight years of age and breed every two to four years thereafter. Males mature at about the same age as females but do not breed until a few years later. Adult polar bears have no natural predators, though walruses and wolves can kill them. Longevity in the wild is 25 to 30 years, but in captivity several polar bears have lived to more than 35 years old.

Humans probably cause most polar bear deaths, by hunting and by destroying problem animals near settlements. Polar bears have been known to kill people. The bears are hunted especially by Inuit people for their hides, tendons, fat, and flesh. Although polar bear meat is consumed by indigenous people, the liver is inedible and often poisonous because of its high vitamin A content.


US Coast Guard to Send Icebreaker to Arctic for National Security

The US Coast Guard’s only long-range icebreaker, the Polar Star, would typically head to the Antarctic to help with the resupply of the McMurdo Station.

However this year’s resupply mission is cancelled due to the COVID-19 pandemic. So this year, the ship will be heading to the opposite end of the world – the Arctic Ocean.

This will be the first time since 1994 that a US Polar-class icebreaker will head to the Arctic on a non-science mission.

The U.S. Coast Guard icebreaker USCGC Polar Star (WAGB-10) at anchor near Palmer Station, Antarctica, in 1983.

The Polar Star will be working in the Arctic to protect the United States’ “maritime sovereignty and security in the region.”

According to Vice Admiral Linda Fagan, the US Coast Guard Pacific Area commander, the Arctic is no longer considered a frontier and is instead thought of as an area of growing importance to the US. Fagan said that the US Coast Guard “is committed” to the protection of US sovereignty in the area and also to cooperating with others to protect the maritime rules of the Arctic.

In 1994, the Polar Sea became one of the first two US surface ships to reach the North Pole.

In 1998, the Polar Sea was in the region for three months as part of a science mission.

In 2009, the Polar Sea again spent three months in the Arctic on another science mission.

This time though, the Polar Star will be in the region for national security purposes and for national sovereignty in the region.

The Polar Star was last in the Arctic in 2013 for sea trials after receiving a $57 million overhaul.

Russia, the largest Arctic nation, and China have both been increasing their activity in the region and seeking to expand their influence there. The US is looking to retain its own authority in the Arctic.

Keeping a presence in the Arctic hasn’t been easy for the Coast Guard lately. Their fleet of icebreakers was already insufficient but there have been losses which have reduced their numbers even further. New ships are not expected for another few years.

The medium icebreaker, the Healy Coast Guard, experienced a crippling fire in one of the main propulsion motors. The ship was able to limp back to port in Washington under its own power. The ship was originally heading to the Arctic for a deployment that was to last until October.


Disabled fishing vessel Antarctic Chieftain is towed astern of the Coast Guard Cutter Polar Star through sea ice near Antarctica, Feb. 14, 2015

The Polar Star has not been exempt from its own problems. Last year, it had its own engine fire which damaged the garbage incinerator housing and the effort to contain the fire caused damage to the electrical system. The ship is in good shape this year after receiving a few repairs and is scheduled to head to the Arctic in December.

The resupply for McMurdo this year will use aircraft.

The Navy and Coast Guard gave a $749.5 million contract to VT Halter Marine in Pascagoula, Mississippi, for the first of three new heavy icebreakers which are known as Polar Security Cutters. Construction on the new ship should begin next year.


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