MOON, tuna, Q , in astronomy, a satel lite, or secondary planet, always attendant on our earth.
The moon being the nearest, and, next to the sun, the most remarkable body in our system, and also useful for the divi sion of time, it is no wonder that the an cient astronomers were attentive to dis cover its motions, and the orbit which it describes.
The motion of the moon in its orbit about the earth is from west to east, and its orbit is found to be inclined to the ecliptic. The motion of the moon is also observed not to be uniform, and its distance from the earth is found to vary, which spews that it does not re volve in a circle about the earth in its centre ; but its motion is found to be in an ellipse, having the earth in one of the foci. The position of the ellipse is ob served to be continually changing, the major axis not being fixed; hut moving sometimes direct and sometimes retro. grade : but, upon the whole, the motion is direct, and it makes a complete revolution in a little more than eight years and a half. The eccentricity of the ellipse is also found to change, that is, the ellipse is sometimes nearer to a circle than it is at other times. The inclination of its orbit is found likewise subject to a varia tion from 5' to 5. 18'. All these irrcgu larities :ride from the sun disturbing the moon's motion by its attraction. As the ellipse which the moon describes about the sun is subject to a variation, the pe riodic time of the moon about the earth will also vary . in winter the moon's orbit is dilated, and the periodic time is in creased; and in summer, her orbit is con tracted, and her periodic time dimi nished. The periodic time of the moon increases whilst the sun is moving from bis apogee to hisperigee, and decreases whilst he moves from his perigee to his apogee ; and the greatest difference of the periodic times is found to be about twenty-two minutes and a half. The mean periodic time of the moon is 27d 43' 11", 5 ; this is called her sidereal revolution, being the mean time from her leaving any fixed star till her return to it again. Now it is found by observation, that the mean time from her leaving her apogee till she returns to it, is 27d 13h 18'4"; hence the moon is longer in re turning to her apogee than she is in mak ing a revolution in her orbit, and there. fore her apogee must move forward. The mean time for her leaving her node till she returns to it again, is 27d 5' 35", 6, and this being less than her mean pe riodic time, it follows, that she returns to her node before she has completed her revolution, and therefore her nodes must have a retrograde motion. The time be
tween two mean conjunctions of the sun and moon, or from new moon to new moon, supposing their motions had both been uniform, is found by multiplying the periodic times of the earth and moon together, and dividing by their differ ence; taking therefore the mean periodio time of the moon and sun as already stat ed, we get the mean time From conjunc tion to conjunction to be 29d 12h 44' 8, and this is called her synodic revo lution. The true time from new to new moon will be sometimes greater and sometimes less than this.
The apparent diameter of the moon is found continually to vary ; now the appa rent diameter of any very distant body varies inversely as its distance. Hence, as the apparent diameter of the moon in creases, she must approach the earth ; and when it decreases, she must recede from the earth. This variation of her ap parent diameter agrees exactly with what ought to be the case, if the moon moved in an ellipse about the earth in one of its foci ; we conclude, therefore, that the moon moves in an ellipse about the earth situated in one of its foci, as no other sup position will agree with the observed vari ation of the moon's diameter. From the variation of the sun's diameter it appears, in like manner,that the earth must revolve in an ellipse about the sun, having the sun in one of the foci. The earth moving in an ellipse about the sun in its focus, the nearer the earth comes to the sun, the more it is attracted by him, and this at. traction increases in the same ratio as the square of the distance diminishes; and, on the contrary, it decreases as the square of the distance increases. As therefore the earth approaches the sun all the time it moves from the aphelion to the perihelion, the attraction increases, and conspiring partly with the earth's motion, it accele rates the motion of the earth ; and when the earth moves from perihelion to aphe• lion, the attraction acts partly against the earth's motion, and diminishes its motion. Thus, the velocity of the earth increases whilst it moves from the aphelion to peri helion, and decreases as much whilst it moves from perihelion to aphelion.