Which planet, viewed from which other planet would appear the largest?

Question

Inspired by this question, I'm curious: Which planet in our solar system, when viewed from which other planet, would appear the largest/brightest? You probably can't really see much of Uranus from Neptune as that question asked, but could you clearly see any other planet from another planet? (Assuming ideal conditions of both planets being at their closest possible distance from each other, and maybe just from an orbiting satellite around the viewing planet so as to avoid any atmospheric effects.)

And would it appear larger or brighter than just the stars around it? From Earth, all of the planets we can see are near indistinguishable from stars to the untrained eye without a telescope. But if you were closer to them, are there any planets close enough to each other and/or large enough that one could be seen as obviously a planet from the other? I'd bet on Venus from Mercury based on minimal distance, but Jupiter from Mars would be a good contender given how large it is.

Answer 1

Here is a table with planets, their minimum/maximum distances from the Sun, their minimum distance (assuming the planet's aphelion and its neighbour's perihelion coincide, which they don't, so the actual minimum distance is a bit higher), the size of the largest of the two (indicated with a *), and finally the maximum apparent size $s$, which is given by $s = 2 \tan^{-1}\frac{\text{radius}}{\text{minimum distance}}$. All data was taken from Wikipedia.

Planet	Aphelion (AU)	Planet	Perihelion (AU)	Min. distance (AU)	Radius (km)	Max. size (")
Mercury	0.467	Venus*	0.718	0.251	6,052	66
Venus	0.728	Earth*	0.983	0.255	6,371	69
Earth*	1.017	Mars	1.382	0.365	6,371	48
Mars	1.666	Jupiter*	4.950	3.284	69,911	59
Jupiter*	5.459	Saturn	9.041	3.582	69,911	54
Saturn*	10.124	Uranus	18.286	8.162	58,232	20
Uranus*	20.097	Neptune	29.81	9.713	25,362	7

So the Earth as seen from Venus would be the largest, but as Earth has only half the albedo of Venus, Venus as seen from Mercury will probably be brightest (Venus is largest for us if it's in conjunction with the Sun, so 0% illuminated, but for Mercury it happens if it's 100% illuminated). Jupiter from Mars (or Saturn) is definitely smaller.

I've seen other users being able to calculate exact (maximum) brightness and gladly defer to them for that information.

Answer 2

I note that the planet which appears to have the largest angular diameter as seen from Earth is Venus.

Venus, our sister planet, comes closest to Earth, ranging from 9.7" to a whopping 66.0".

https://medium.com/starts-with-a-bang/which-planet-appears-the-largest-from-earth-d95f2f72a8f8

In astronomy " is the symbol for an arc second of angular diameter.

Since a normal human eye can resolve objects as small as about 28 arc seconds, it might be possible to see the shape of Venus when Venus is almost closest to Earth and appears as a very thin crescent at almost its maximum angular diameter, though that would seem to be at the very edge of visibility.

Humans with exceptional vision, at Venus’ closest approach, can barely discern its crescent phase without a telescope.

https://medium.com/starts-with-a-bang/which-planet-appears-the-largest-from-earth-d95f2f72a8f8

My copy of The Guinness Book of Astronomy Facts & Feats, Patrick Moore,second ediiton, 1979, 1983, says that Galileo was the first persons to observe the phases of Venus which were evidence for the validity of the Coppernican theory. And says:

(The phases had not previously been mentioned specifically, though exceptionally keeen-sighted people can see the crescent form with the naked eye.)

Wikipedia says:

The phases of Venus are the variations of lighting seen on the planet's surface, similar to lunar phases. The first recorded observations of them are thought to have been telescopic observations by Galileo Galilei in 1610. Although the extreme crescent phase of Venus has since been observed with the naked eye, there are no indisputable historical pre-telescopic records of it being described or known.1

The extreme crescent phase of Venus can be seen without a telescope by those with exceptionally acute eyesight, at the limit of human perception. The angular resolution of the naked eye is about 1 minute of arc. The apparent disk of Venus' extreme crescent measures between 60.2 and 66 seconds of arc,[6] depending on the distance from Earth.

Mesopotamian priest-astronomers described Ishtar (Venus) in cuneiform text as having horns which has been interpreted as indicating observation of a crescent. However, other Mesopotamian deities were depicted with horns, so the phrase could have been simply a symbol of divinity.1

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

so it is possible that some people have seen the planet Venus as more than a dot in the sky, and even seen its cresent phase.