Changing Appearance of the Moon During a Single Night I have noticed that the inclination of the moon at a given location varies throughout the night. From the UK, the terminator in a half-moon is clearly sloping from top left to bottom right early in the evening, but later on, as the moon is setting, it is clearly sloping from top right to bottom left. I know that the shape of the moon changes from night to night, but I just can't see why the inclination would change during a single night. I know that the appearance of the moon is due to a combination of the tilt of the earth's axis and the latitude of my position (the moon slopes oppositely in the southern hemisphere), but I just can't visualise in three dimensions exactly what is going on. Please can you help me to do this.
If you take a line from the middle of the terminator, but at 90 degrees to the termination, it more or less points towards the sun.  Now consider the moon at first quarter: as the moon rises, the sun is due south, so imagine a line from the moon to the sun, and the terminator will be at 90 degrees to this, so pointing from bottom right to top left.  At mid-day, the sun is in the west, and the terminator will be sloping bottom left to top right.