" . . . You will take
—Thomas Jefferson, Instructions to Meriwether Lewis, 20 June 1803
Thomas Jefferson was together interested in the methods and equipment because that "ascertaining by celestial monitoring the location of the country" together with any type of other solitary aspect the the Expedition. That played an essential role in making sure that Lewis to buy the appropriate equipment and learned just how to usage it before he left for the West. He likewise insisted that monitorings be carried out with accuracy, would be redundant, would certainly be comprehensible come others, and also that sufficient duplicates of all monitorings would be made to guarantee against the possible loss the one or an ext sets. As faithfully as they could, the captains adhered to the President"s wishes.
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Determining Latitude by the phibìc Star
For Lewis and Clark, together for so numerous of your predecessors and also contemporaries, calculating latitude was far much easier than calculating longitude. In the north hemisphere, latitude might be acquired by measure the edge made in between the north Star and the horizon. Crude instruments to achieve this angle have actually existed for countless years and by the moment of Lewis and also Clark, instruments like the sextant and octant, just slightly less specific than those available to us, to be in use.
Figure 1 reflects graphically what an ephemeris shows in tables. The distinction is that the huge almanac gives numbers for solar (sun), lunar (moon), and astral (star) altitudes for every job of the year follow me all currently of latitude conversely, the diagram shows only solar altitude in ~ 4 times throughout the year (equinox and also solstice) and also only follow me one line of latitude. What heat of latitude? That deserve to be established from the diagram listed below as follows: on June 21, in ~ its janice or highest suggest in the sky (local noon) the sunlight is straight overhead (an altitude the 90°) at latitude 23°30" N (the Tropic of Cancer). If the altitude of the noon sun at the point of observation on June 21 is 72°30" (the prize " suggests a "minute," and also 60 minutes equal one degree), climate the latitude the the suggest of monitoring is 41°N. This is obtained from individually 72-1/2 levels (altitude of the sunlight at observation point) native 90 degrees (altitude of sun at Tropic the Cancer) and then including the an outcome (17-1/2 degrees) come the latitude of the Tropic the Cancer (23-1/2 degrees) where the sun"s altitude is 90°. To use the ephemeris, every one requirements to know is the work of the year and the altitude of the sun, the moon, or one of the key stars such together Betelgeuse, Aldebaran, Antares, or Vega.
Latitude may likewise be calculated by measuring the altitude of the sun, moon, or particular planets and also stars above the horizon on recognized days and also reading latitude from tables designed for that purpose. It to be not lot more challenging for the captains to measure these altitudes with a sextant or octant and also to calculation latitude using one of the three ephemerides or expensive almanacs lock carried. These had tables showing the day-to-day position the celestial bodies such as the sun, the moon, and key stars. Calculating latitude offered Lewis and Clark few problems and their readings were specific to in ~ a portion of a degree.
In figure 2, an illustration indigenous a 16th century portolan atlas, a seaman is identify latitude making use of a cross-staff. This maker allowed the to measure the "altitude" the Polaris or the north Star. Polaris is directly overhead in ~ the north Pole (90° of latitude); in other words, the angle between Polaris and the horizon in ~ the phibìc Pole is 90°. This edge is called "the altitude" that Polaris. In ~ the Equator (0° that latitude), the north Star is top top the horizon, do an edge of 0°.
For any suggest between the Equator and the phibìc Pole, latitude is obtained simply by measure the altitude of Polaris: in ~ 30°N the star is 30° above the horizon, in ~ 63°N, the is 63° over the horizon, and also so on. Before the use of the cross-staff pictured, mariners and others who necessary to recognize latitude used level pieces that wood through holes to sight through to locate Polaris and also with pieces of cord attached to measure up angles.
Longitude and also Time
For lot of the at an early stage era of worldwide exploration, longitude had been difficult to calculate due to the fact that either an elaborate set of expensive tables and also measurements were required or precise time-keeping device was necessary, and neither was available until the 18th century. As beforehand as 1610 Galileo had devised a means to determine longitude by monitoring of the passage of the 4 moons of Jupiter.
By the early 18th century, if still utilizing the transit that Jupiter"s moons, navigators had actually learned to do approximate calculations of longitude through observing the changing angular distance in between the Moon and also a prominent star such as Antares. But numerous mindful observations and extensive calculations were required for this an approach to work and neither of these was really feasible on board ship or in the field.
Finally, in 1735, partially in solution to an market of £20,000 by the British government to anyone who could solve the difficulty of determining longitude at sea, one English clockmaker named John Harrison devised a functioning spring-based chronometer that verified promise of a solution. Countless sea trials and several enhanced versions the Harrison"s original design were forced before, in 1773, Harrison had a functioning chronometer, durable enough for comprehensive field observation. It was a variation of this chronometer the Lewis and also Clark brought with them.
All this seems rather simple. Why, then, to be the captain"s longitudinal observations so vulnerable to error? The prize is additionally simple: castle did no have, as we do, reliable battery-powered watches with quartz movements. As soon as their chronometer ran down, it had to be re-calibrated on local time, which forced them to make monitorings to identify the sun"s zenit or regional "noon" and then setting the chronometer through estimating the Expedition"s present longitudinal position. Over the course of your journey, the tiny incremental errors created by this procedure ended up being larger ones.
There to be other techniques of calculating longitude available to them, using expensive observation. But many huge readings had to be acquired over the course of a night in order to achieve sufficiently an exact data to determine longitude. It was asking a lot because that men exhausted by the rigors the their daily trek, to spend three or four hours in the cold and also damp the a hill night acquisition sightings that the moon and also stars, recording observations, and also making calculations by firelight. It to be only herbal that errors would certainly exist in data acquired in this manner. Also the most expert astronomer or surveyor would have been hard pressed to make extremely accurate observations under such circumstances.
Longitude have the right to be calculated utilizing either time or expensive observation. Calculating longitude through chronometer is based upon the truth that any allude on the earth"s surface ar moves through a complete circle the 360 levels once in a 24-hour period; during 1 hour, any suggest on the earth"s surface moves with an east-to-west 15° arc the a full circle. If time can be fixed along any kind of meridian the longitude, climate longitudinal distance deserve to be identified by compare time at the meridian with regional time, usually based upon the allude at which the sun reaches the zenith.
From number 3 it have the right to be checked out that if it is noon along the prime or Greenwich meridian of longitude, it will certainly be 1:00 pm 15° to the east and also 11:00 am 15° come the west. These times are referred to respectively together being "ahead" or "behind" Greenwich average Time (GMT), or time along the prime meridian. Making use of this principle, the is basic to recognize longitude. For example, if a chronometer set on Greenwich typical Time reads 6:00 pm or 1800 GMT at the time once the sun reaches that is highest point in the skies (local noon) native the vantage allude of the observer, then the sun reached its zenith end the element meridian 6 hours earlier. The observer is, therefore, 90° west of prime meridian (6 hours x 15° = 90° the longitude). Because local sunlight time is different everywhere indigenous GMT, trying to keep track the train schedule on east-west routes ended up being impossible by the mid-19th century and also so, by global convention in 1877, standard time zones of about 15° the longitudinal width were established, centered on 0°, 15°E and also W, 30°E and also W, and also so on. Within every time zone, time is the same everywhere, fairly than being preserved locally.
The errors the Lewis and Clark made in latitude and longitude calculations were much less the an outcome of your instruments, your mathematics, or field conditions than by small errors that three types that affect all expensive observations:
(1) miscalculating refraction or the bending of light in the atmosphere, which causes altitudes to show up slightly greater than they actually are;
(2) estimating semidiameter of either the sun or moon, the discs that which are too large to be used whole when making a sighting. As such it is crucial to sight the "sun"s upper limb" or top fifty percent or the "moon"s lower limb" or bottom half and climate correct by calculation to achieve a reading at the facility of the disc; and
(3) correcting for "parallax," the truth that when navigational tables are based on distances and also angles calculated indigenous the earth"s center, observations are make from the earth"s surface.
" . . . That they may with certainty be recognised hereafter."
—Thomas Jefferson, Instructions come Meriwether Lewis, 20 June 1803
After the expedition Jefferson noted that "it is just to latitudes that
Clark"s last map to be the finishing piece of geographical information arising from the Expedition and also resulting directly from Jefferson"s injunction come preserve expertise for the future. Perfect in manuscript type by 1811, engraved and also published v the Biddle History that the expedition . . . in 1814, it portrayed with artistry, skill, and also accuracy the area through which the expedition had passed. Course and distance information is evident on the map and also coordinate positions are precise to within 5%, an accuracy level that would not be suitable by plenty of cartographers until the advent of mapping aided by aerial photography in the beforehand 20th century.
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Clark"s map represented the can be fried triumph that the upright perspective, the capability to synthesize mental and also actual maps and to portray geographical features with precision in the paper definition of the geographic coordinate mechanism within which the operated.