Significance of Lunar phases from observer’s point of view
Most astronomical diaries give date and times of the new moon and full moon phases along with first and the last quarter phase.
We know that a few days before and after the full moon it is nearly impossible to watch faint stars and extended objects like galaxies, nebulae etc. And a period of couple of days before and after the new moon phase is really good time to do observations of such objects.
Well the first quarter phase of the moon is when it is halfway between the new moon phase and full moon phase, where as the last quarter of the moon is when it is between the full moon and new moon day.
On these quarter moon phase we see half illuminated lunar disk. But this information also tells us two significantly important aspects related to observations. Firstly the moon is close to the observers meridian or (nearly) over head at sunset or sunrise. Secondly if it is the first quarter then the moon will set close to local midnight or will rise close to the midnight on the last quarter.
How do we make use of this information?
Suppose you are planning to go away from your city for a weekend observations of the deep sky objects. Say this happens to be close to the first quarter of the moon. You know that you will have moon light in the sky for some hours after the sun has set. You can start your real observations at midnight. You can spend this time to take a quick nap or do something else.
On the other hand if the outing day is close to the last quarter then you better hurry up and reach your observing spot well in time so that you make maximum use of the dark night available to you.
Similarly if your weekend observing outing is closer to the last quarter you can pack up early and be home in good time.
Of course these are general directives to keep in mind. For serious stuff you will have to plan more systematically.
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