Exercise 15.—Find the present positions of Jupiter and Saturn, and look them up in the sky by means of your star maps. The planets will appear in the indicated constellations as very bright stars not shown on the map.
Which of the planets, Jupiter and Saturn, changes its direction from the sun more rapidly? Which travels the greater number of miles per day? When will Jupiter and Saturn be in the same constellation? Does the earth move faster or slower than Jupiter?
The distance of Jupiter or Saturn from the earth at any time may be readily obtained from the figure. Thus, by direct measurement with the millimeter scale we find for January 1, 1900, the distance of Jupiter from the earth is 6.1 times the distance of the sun from the earth, and this may be turned into miles by multiplying it by 93,000,000, which is approximately the distance of the sun from the earth. For most purposes it is quite as well to dispense with this multiplication and call the distance 6.1 astronomical units, remembering that the astronomical unit is the distance of the sun from the earth.
Exercise 16.—What is Jupiter's distance from the earth at its nearest approach? What is the greatest distance it ever attains? Is Jupiter's least distance from the earth greater or less than its least distance from Saturn?
On what day in the year 1906 will the earth be on line between Jupiter and the sun? On this day Jupiter is said to be in opposition—i. e., the planet and the sun are on opposite sides of the earth, and Jupiter then comes to the meridian of any and every place at midnight. When the sun is between the earth and Jupiter (at what date in 1906?) the planet is said to be in conjunction with the sun, and of course passes the meridian with the sun at noon. Can you determine from the figure the time at which Jupiter comes to the meridian at other dates than opposition and conjunction? Can you determine when it is visible in the evening hours? Tell from the figure what constellation is on the meridian at midnight on January 1st. Will it be the same constellation in every year?
30. Mercury, Venus, and Mars.—[Fig. 17], which represents the orbits of the inner planets, differs from [Fig. 16] only in the method of fixing the positions of the planets in their orbits at any given date. The motion of these planets is so rapid, on account of their proximity to the sun, that it would not do to mark their positions as was done for Jupiter and Saturn, and with the exception of the earth they do not always return to the same place on the same day in each year. It is therefore necessary to adopt a slightly different method, as follows: The straight line extending from the sun toward the vernal equinox, V, is called the prime radius, and we know from past observations that the earth in its motion around the sun crosses this line on September 23d in each year, and to fix the earth's position for September 23d in the diagram we have only to take the point at which the prime radius intersects the earth's orbit. A month later, on October 23d, the earth will no longer be at this point, but will have moved on along its orbit to the point marked 30 (thirty days after September 23d). Sixty days after September 23d it will be at the point marked 60, etc., and for any date we have only to find the number of days intervening between it and the preceding September 23d, and this number will show at once the position of the earth in its orbit. Thus for the date July 4, 1900, we find
1900, July 4 - 1899, September 23 = 284 days,
and the little circle marked upon the earth's orbit between the numbers 270 and 300 shows the position of the earth on that date.
In what constellation was the sun on July 4, 1900? What zodiacal constellation came to the meridian at midnight on that date? What other constellations came to the meridian at the same time?
The positions of the other planets in their orbits are found in the same manner, save that they do not cross the prime radius on the same date in each year, and the times at which they do cross it must be taken from the following table: