| H. | M. | S. | T. | ||
|---|---|---|---|---|---|
| Deg. | 150 | 10 | 0 | 0 | 0 |
| 3 | 12 | 0 | 0 | ||
| Min. | 51 | 3 | 24 | 0 | |
| Sec. | 5 | 20 | |||
| Answer | 10 | 15 | 24 | 20 | |
CHAP. XII.
Of Solar and Sidereal Time.
Sidereal days shorter than solar days, and why.
221. The fixed Stars appear to go round the Earth in 23 hours 56 minutes 4 seconds, and the Sun in 24 hours: so that the Stars gain three minutes 56 seconds upon the Sun every day, which amounts to one diurnal revolution in a year; and therefore, in 365 days as measured by the returns of the Sun to the Meridian, there are 366 days as measured by the Stars returning to it: the former are called Solar Days, and the latter Sidereal.
The diameter of the Earth’s Orbit is but a physical point in proportion to the distance of the Stars; for which reason, and the Earth’s uniform motion on it’s Axis, any given Meridian will revolve from any Star to the same Star again in every absolute turn of the Earth on it’s Axis, without the least perceptible difference of time shewn by a clock which goes exactly true.
If the Earth had only a diurnal motion, without an annual, any given Meridian would revolve from the Sun to the Sun again in the same quantity of time as from any Star to the same Star again; because the Sun would never change his place with respect to the Stars. But, as the Earth advances almost a degree eastward in it’s Orbit in the time that it turns eastward round its Axis, whatever Star passes over the Meridian on any day with the Sun, will pass over the same Meridian on the next day when the Sun is almost a degree short of it; that is, 3 minutes 56 seconds sooner. If the year contained only 360 days as the Ecliptic does 360 degrees, the Sun’s apparent place, so far as his motion is equable, would change a degree every day; and then the sidereal days would be just four minutes shorter than the solar.
Fig. II.
Let ABCDEFGHIKLM be the Earth’s Orbit, in which it goes round the Sun every year, according to the order of the letters, that is, from west to east, and turns round it’s Axis the same way from the Sun to the Sun again every 24 hours. Let S be the Sun, and R a fixed Star at such an immense distance that the diameter of the Earth’s Orbit bears no sensible proportion to that distance. Let Nm be any particular Meridian of the Earth, and N a given point or place upon that Meridian. When the Earth is at A, the Sun S hides the Star R, which would always be hid if the Earth never removed from A; and consequently, as the Earth turns round it’s Axis, the point N would always come round to the Sun and Star at the same time. But when the Earth has advanced, suppose a twelfth part of it’s Orbit from A to B, it’s motion round it’s Axis will bring the point N a twelfth part of a day or two hours sooner to the Star than to the Sun; for the Angle NBn is equal to the Angle ASB: and therefore, any Star which comes to the Meridian at noon with the Sun when the Earth is at A, will come to the Meridian at 10 in the forenoon when the Earth is at B. When the Earth comes to C the point N will have the Star on it’s Meridian at 8 in the morning, or four hours sooner than it comes round to the Sun; for it must revolve from N to n, before it has the Sun in it’s Meridian. When the Earth comes to D, the point N will have the Star on it’s Meridian at six in the morning, but that point must revolve six hours more from N to n, before it has mid-day by the Sun: for now the Angle ASD is a right Angle, and so is NDn; that is, the Earth has advanced 90 degrees in it’s Orbit, and must turn 90 degrees on its Axis to carry the point N from the Star to the Sun: for the Star always comes to the Meridian when Nm is parallel to RSA; because DS is but a point in respect of RS. When the Earth is at E, the Star comes to the Meridian at 4 in the morning; at F, at two in the morning; and at G, the Earth having gone half round it’s Orbit, N points to the Star R at midnight, being then directly opposite to the Sun; and therefore, by the Earth’s diurnal motion the Star comes to the Meridian 12 hours before the Sun. When the Earth is at H, the Star comes to the Meridian at 10 in the evening; at I it comes to the Meridian at 8, that is, 16 hours before the Sun; at K 18 hours before him; at L 20 hours; at M 22; and at A equally with the Sun again.
A Table, shewing how much of the Celestial Equator passes over the Meridian in any part of a mean Solar Day; and how much the Fixed Stars gain upon the mean Solar Time every Day, for a Month.