How can we see Venus at night? [closed]

Question

According to the Globe Earth Theory, the Sun is in the middle of the Solar System and the Earth is the 3rd planet from the Sun, making Mercury and Venus between Earth and the Sun. If this is true, Mercury and Venus should only be seen from the lit side of the planet, since it is always between the Sun and Earth. How can you see it at night?

Answer 1

Before we begin: how far a planet is seen from the Sun is called elongation, and it's measured in degrees. 0° elongation means it's right on top of the Sun (or behind); 180° elongation means it's opposite to the Sun (it's highest in the sky at midnight, when the Sun is on the other side of the Earth).

https://en.wikipedia.org/wiki/Elongation_(astronomy)

See the image below, where the Sun and the Earth are shown, along with an inferior planet (such as Mercury) and a superior planet (such as Mars). Elongation is the angle marked ε.

How can you see it at night?

Both Venus and Mercury are always seen close to the Sun. You can never see them at midnight, true. But you can see them during twilight, or, in Venus' case, shortly after nightfall (and then it sets quickly), or shortly before dawn in the morning (and then it's masked by the light of day). This is not a paradox or an impossibility. Here's why:

Mercury in particular can only be seen during twilight, very close to sunset or sunrise. Its orbit is so close to the Sun in space (only 39% the size of Earth's orbit), it does appear very close to the Sun even in the sky as seen from Earth. You could not see it during the day, of course, because the sky is so bright. But during twilight you can sometimes see it peeking just to the side of the Sun, very briefly - then it either sets in the West, or is swallowed by the light of day.

The greatest elongation that Mercury can achieve is 28°. Hold your arm straight out in front of you and make a fist; twice the size of your fist is nearly 28°. But even that's quite exceptional; most of the time Mercury stays closer to the Sun, closer than half of that angle (less than one fist).

So I should make it very clear: it's very rare that you can actually see Mercury with your naked eyes. It pretty much has to be right at maximum elongation. I've observed its phases (just like the Moon, or Venus) in a small dobsonian telescope a couple times; at max elongation it's close to the first quarter phase, or last quarter, and it looks like a very tiny replica of the Moon seen at that same phase. Kind of like this (except in my small telescope no craters or mountains were visible, because the image was just too tiny):

https://en.wikipedia.org/wiki/Planetary_phase

Venus' orbit is quite a bit wider, about 72% the size of Earth's own orbit. So it can swing ahead or behind the Sun quite widely. But that's all it can do - swing ahead or behind. It can never go "all the way around" the Earth. You can never see it at midnight, when the Sun is on the other side of Earth.

Venus' maximum elongation is 47°. Stretch your arm out and make a fist; now stick your thumb and your pinky sideways as far as they go (like the "hang loose" gesture, but stick them out all the way). The span from tip to tip is about 25°; twice that span is the maximum elongation of Venus.

Now imagine Venus at maximum elongation - two "hang loose" hand spans. The Sun has already set in the West about 1 hour and 40 minutes ago, so this is during the night, it's dark already, and now the Sun is one "hang loose" hand span below horizon. But Venus is at maximum elongation, which means it's one handspan above horizon. That's quite hight in the sky actually, you can see it pretty well.

So, there you have it. You can actually see Venus during the night. Not for long, because it still can't wander off too far from the Sun. It must remain within two "hang loose" hand spans from the Sun, or less than that distance, at all times. So Venus itself will set in the West soon after you see it. It cannot hang around until midnight.

Venus also shows phases, just like the Moon or Mercury. I've watched those too in my telescopes.

You can get more precise angle measurements if you can use an old-school marine sextant, like captains on ships back in the day. The fist and "hang loose" gesture techniques are just approximations. Or just get a protractor and tape two straws to it at the desired angle, and sight along the straws to estimate the angle in the sky.

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The superior planets (Mars, Jupiter, etc) are not like that. Their orbits are larger than Earth's own orbit. So they can actually be seen, once in a while, high in the sky at midnight, when the Sun is on the opposite side of Earth.

Please refer to the diagram at the top of this reply, it's quite self-explanatory.

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So, as you can see, the standard solar system model in astronomy is in excellent agreement with what you can see with your own eyes. There is no disagreement between observation and the model - if there was, the model would be fixed. That's how science works.

Answer 2

We can see Venus at night (dusk) and in the morning (predawn), just not all night or every night.

We need some geometry to understand this, and it boils down to tangents.

I've shamelessly borrowed this diagram from a paper to show the idea. It's discussing Mercury, but it's the same idea for Venus.

We'll simplify things by using the pretty good approximation that Earth and Venus have circular orbits. We'll also assume Earth is a perfect sphere - another good approximation. We're also assuming Earth's rotation is not at an angle to the plane of it's orbit (that's the worse approximation !). Finally we're going to assume the orbits are not inclined (not a bad approximation, but not strictly true).

The maths would get messy if we didn't do those things, so it turns out that the maths works out that the number of degrees that's the maximum the Earth can rotate through and still see Venus after the sun goes down is approximately :

$$\theta = 90^\circ-cos^{-1}\left(\frac {r_{venus}} {r_{earth}}\right)$$

Now $\frac {r_{venus}} {r_{earth}} \approx 0.72$ and this means $\theta \approx 46^\circ$

If you think about $46^\circ$ of rotation out of a quarther circle that's slightly more than half, and a quarter circle's worth of rotation of the Earth is about 6 hours, so that angle represents our ability to see Venus for (at most) three hours after sunset and three hours before sunrise.

This is also discussed in this article.

The technical term for these angles is elongation. The actual maximum elongation is slightly over $47^\circ$ so the simplifications didn't do much damage to our estimate ! As it happens this year (in January) we had an elongation of Venus that was almost the maximum. It varies (due to the factors we simplified) between $45^\circ$ and and slightly over $47^\circ$.