Page images
PDF
EPUB

south pole will measure an arc bC' more than if he were located at E, the centre of the earth. The sum of bG' and bC' = G'C is the difference in the position of the moon as seen from the two stations. In other words, it is the moon's parallax. The arc G'C measures the angle C'MG'; that angle is equal to the opposite angle GMC = Now, in the foursided figure GECM, the sides GE and CE are each equal radii of the earth = 3956 miles; while the distance from G to 0 is the difference in the latitude of the two places. The angles ZGM and Z'CM, being the zenith distances of the moon, are known, and so the angles MGE and MCE are easily found. EM, the moon's distance from the centre of the earth, is thus readily computed by a simple trigonometrical formula.

(3.) The horizontal parallax of the moon is most commonly found by estimating its distance, not from the north and south poles, as just explained under the general meaning of the term parallax, but from a fixed star. The moon's horizontal parallax is now estimated at 57', which makes its distance about sixty times the earth's semi-diameter.*

TO FIND THE SUN'S DISTANCE FROM THE EARTH.—

This might be estimated by obtaining the solar

* In figure 95, let 8 represent the moon, sun, or any other heavenly body, AB the semi-diameter of the earth, and A8B the "horizontal parallax" of the body. Then, by the following trigonometrical formula, the distance from the earth may be easily calculated—

AS : AB :: Radius : Sin of ABB.

parallax in the same maimer as the lunar parallax. It would be only necessary to take the sun's distance from the north and south poles respectively at Greenwich and the Cape of Good Hope, and then subtracting 180° from the sum of the two angular distances, the remainder would be the solar parallax. The difficulty in this method lies in the fact that when the sun shines the air is full of tremulous motion. This increases refraction—that plague of all astronomical calculations—to such an extent that it becomes impossible to calculate so small an angle with any accuracy. Neither can the parallax be estimated, as in the case of the moon, by measuring

[ocr errors][graphic]

the distance from a fixed star, since when the sun shines the stars near by are invisible even in a telescope. Astronomers have therefore been compelled to resort to other methods.

(1.) Calculation of solar parallax by observation of the planet Mars.—We have already seen that the distance of Mars from the sun is $ that of the earth from the sun. If, therefore, we can find Mars' distance from the earth, we can multiply it by three, south pole will measure an arc bC' more than if he were located at E, the centre of the earth. The sum of bG' and bC = Q'C is the difference in the position of the moon as seen from the two stations. In other words, it is the moon's parallax. The arc G-C measures the angle C'MG'; that angle is equal to the opposite angle GMC = 1£°. Now, in the fourBided figure GECM, the sides GE and CE are each equal radii of the earth = 3956 miles; while the distance from G to C is the difference in the latitude of the two places. The angles ZGM and Z'CM, being the zenith distances of the moon, are known, and so the angles MGE and MCE are easily found. EM, the moon's distance from the centre of the earth, is thus readily computed by a simple trigonometrical formula.

(3.) The horizontal parallax of the, moon is most commonly found by estimating its distance, not from the north and south poles, as just explained under the general meaning of the term parallax, but from a fixed star. The moon's horizontal parallax is now estimated at 57', which makes its distance about sixty times the earth's semi-diameter.*

To FIND THE SUN'S DISTANCE FROM THE EARTH.—

This might be estimated by obtaining the solar

* In figure 95, let S represent the moon, sun, or any other heavenly body, AB the semi-diameter of the earth, and ASB the "horizontal parallax" of the body. Then, by the following trigonometrical formula, the distance from the earth may be easily

calculated—

AS : AB :: Radius : Sin of ASB.

parallax in the same manner as the lunar parallax. It would be only necessary to take the sun's distance from the north and south poles respectively at Greenwich and the Cape of Good Hope, and then subtracting 180° from the sum of the two angular distances, the remainder would be the solar parallax. The difficulty in this method lies in the fact that when the sun shines the air is full of tremulous motion. This increases refraction—that plague of all astronomical calculations—to such an extent that it becomes impossible to calculate so small an angle with any accuracy. Neither can the parallax be estimated, as in the case of the moon, by measuring

Fig. 86.

[graphic]

the distance from a fixed star, since when the sun shines the stars near by are invisible even in a telescope. Astronomers have therefore been compelled to resort to other methods.

(1.) Calculation of solar parallax by observation of the planet Mars.—We have already seen that the distance of Mars from the sun is $ that of the earth from the sun. If, therefore, we can find Mars' distance from the earth, we can multiply ifc by three, and so obtain the distance of the sun from the earth. In 1862, when Mars was in opposition, it came very near ns, for it was in perihelion while the earth was in aphelion, so that its distance (as since ascertained) was only 126,300,000 - 93,000,000 = 33,300,000 miles. Observers at Greenwich ard the Cape, and at various American and European observatories, calculated the distance of the planet from the north and south poles, as well as from several fixed stars, in precisely the manner just explained for obtaining the lunar parallax. The result of these observations fixed the solar parallax at 8.94".*

(2.) Calculation of solar parallax by observation of the transit of Venus.—In the figure, let A and B represent the positions of two observers stationed at

Fig. 96.

[graphic][ocr errors][merged small]

opposite sides of the earth. At the time of the transit, the one at A will soe the planet Venus as a round black spot at V" on the sun's disk, while the one at B will see it at V. The distance V'V" is the

* By the formula on page 302, we have—

4.8 : AB :: Radius : Sin 8.04".

« PreviousContinue »