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    Re: Location of Venus
    From: Frank Reed
    Date: 2021 Mar 11, 16:37 -0800

    Bob Goethe, you asked:
    "Is Venus physically in front of the sun, or behind the sun from us?" 

    Venus is behind the Sun, or at "superior conjunction". It was aligned with the Sun on the near side at "inferior conjunction" on June 3 last year. You may recall we talked a lot about seeing Venus in daylight in April and then again in August. We haven't talked about it since then because Venus has been on the far side of its orbit. It will be back to inferior conjunction after 584 days, the "synodic period of Venus", which is just about 19 months. That is, in early January of 2022 Venus will be at inferior conjunction again. Notice that the circumstances in January next year will be quite different. The Sun, and therefore the inferior conjunction with Venus, is at high northern latitude in early June but at deep southern latitude (declination) in early January. So it won't be at all easy to see Venus in daylight from mid-northern latitudes at the next pass in front of the Sun.

    In addition to the synodic period, which all planets possess, Venus also has a special cycle. It repeats its positions almost perfectly every eight years. So if you want to repeat all the fun of the late Spring of 2020, you can sit back and wait for 2028. In that year, Venus will be easy to see in daylight in mid-northern latitudes in April and August and it will hit inferior conjunction again in early June.

    You added: "And what is the best way to answer that sort of question going forward?"

    You get on the phone with a friend living on Venus. Time the delay in seconds between your "hello" and your friend's reply. That light travel time delay in seconds divided by 500 gives you the distance to Venus in AUs. The minimum distance from Earth in AUs is about 0.3. The maximum is about 1.7. Recall that 1AU, "astronomical unit", is the Earth's mean distance from the Sun. The AU is a standard scale unit for planetary dynamics and is approximately 93 million miles of 149 million km.

    What? You don't have a friend on Venus? Or your friend doesn't have an interplanetary dialing plan? OK, then. How can you tell from commonly accessible almanac data? First if your almanac provides parallax values for the planets, they correspond directly to the distance to the planet. The geocentric parallax of Venus or Mars (or any other object within the Solar System) is equal to 9"/(dist in AU). Equivalently, then, the distance in AUs is 0.15'/pax. So suppose you look up the parallax of Venus and an almanac says that it is presently 0.3'. The distance is then 0.15/0.3 which is 0.5 AU, relatively close to the Earth.

    You can also check whether Venus is near or far from the Earth by looking at the rate of change of GHA or SHA. When Venus is passing through inferior conjunction, it's zipping along changing its GHA by a degree and a half per day. At superior conjunction it's moving almost ten times more slowly, changing its GHA by only about 10' in one day.

    But by far the best way to know what Venus is up to is to keep track of the last inferior conjunction (or any event like this) and add 19 months. It's simple, and you have plenty of time to update later. And don't forget the eight-year cycle. That helps a great deal when you're thinking about opportunities to use Venus in celestial navigation. Not all inferior conjunctions are created equal... unless you wait eight years.

    Note: the synodic period is not the orbital period of the planet. Since Venus and the Earth are both orbiting, it takes much longer than one Venus year or one Earth year for the Earth to catch up to Venus. This is a lot like the hands on an analog clock. The hands align every day at noon, but they don't align again exactly an hour later. Instead they align again a little after 1:05pm. The interval is about 65.5 minutes. Similarly the period for the Venus and Earth "hands" of the Solar System clock to line up is 19 months. 

    Frank Reed

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