## What are four phases of the lunar cycle?

There is a category name corresponding to the phases name.
print(lunar.4phases)
[1] "New"    "Waxing" "Full"   "Waning"

### Eight category labels of the moon for lunar phase.

print(lunar.8phases)
[1] "New"             "Waxing crescent"
[3] "First quarter"   "Waxing gibbous"
[5] "Full"            "Waning gibbous"
[7] "Last quarter"    "Waning crescent"

### How to get the lunar phase on a specific date?

lunar.phase(as.Date("2013-05-06"))
[1] 5.507184
print(terrestrial.seasons)
[1] "Winter" "Spring" "Summer" "Autumn"

#Distance to the moon is returned in units of earth radii, or as a 5-level factor variable referring to the moon's perigee (at about 56 earth radii) and apogee (at about 63.8 earth radii).
> lunar.distance(as.Date("2004-03-24"))
[1] 62.87136
.>lunar.distance.mean(x, towards = -6, ..., by = c("date", "hours", "day","night"))
lunar.distance.mean(as.Date("2004-03-24"))
[1] 61.10886

#### lunar.illumination(x, shift = 0)

> lunar.illumination(as.Date("2004-03-24"))
[1] 0.1189133

### Intersection of subring

How to prove the intersection of two subrings is a subring? Let S1 and S2  be two subrings of a ring R. Then S1∩S2 is not empty since ...