What celestial mechanics parameters define a lunar occultation of Venus visible from Earth?

Question

As a carry on from the following thread Are lunar occultations visible to the naked eye?

Is it correct that the following parameters must hold true if we use Moon occult Venus as an example

1. [Long_Moon = Long_Venus = RA_Moon = RA_Venus] AND [DEC_Moon = DEC_Venus]
2. Moon and Venus must both be visible, i.e. not too close to the Sun

I expect both of these events will need to occur above the horizon (ascendant) for the location right?

Am I missing anything? Are there agreed parameters for degrees above the horizon for visibility?

Like eclipses, such events wont be observed everywhere on earth. Is there an orb convention that captures when occultations can be observed on earth? Is there a way to identify where on earth the total occultation can be observed?

Thank you for any guidance with this.

Answer 1

A lunar occultation of Venus happens when light from Venus can not reach the observer because the Moon blocks it.

The simplest model for this would be to draw a line in 3D from Venus to the observer and detect when that line passes through some part of the Moon. However that doesn't take into account the time it takes for the light to travel from Venus to the observer for example.

Angular separation

If you have apparent positions in RA and Dec as seen from the observer, then those take care of several corrections.

In that case, the Moon will occult Venus from the viewpoint of the observer when the angular separation between their centers is smaller than the angular radius of the Moon, which is very roughly 1/4 of a degree but changes a lot during the month because the Moon's orbit is elliptical.

Above horizon

You need to make sure they are far enough above the horizon to be visible to the observer. If the location has a flat, dark horizon, perhaps only a handful of degrees is sufficient. If in an urban setting then it may need to be 10 or 20 degrees to clear the lights and buildings, or more.

Visibility (when above horizon)

To be visible by eye is a tough call. Venus is always roughly magnitude -4 (-3.8 to -4.8) and so if it were daytime and passing behind the dark edge of the Moon, it might be visible in the daytime to a careful observer with excellent eyesight since they know exactly where to look for it. Looking through a cardboard tube to block other light might help, and certainly as you mention the farther the angular separation from the Sun at the time the better! But this is pretty rare and many people would not see it easily.

With binoculars or a telescope it will be a lot easier to see in the daytime, since magnification reduces the surface brightness of extended objects (like the Moon and the sky) relative to unresolved objects as Venus would be in a relatively low magnification view.

If Venus were passing behind the bright edge of the Moon, this might also be difficult to see by eye. The surface brightness of the moon is about -6 magnitude per square arc minute (the apparent size of Venus for less-than-perfect vision) which is way brighter than what Venus looks like, so it's going to be a real challenge to see this situation by eye.

But again with binoculars or a telescope this will be a lot easier.