
An unimaginable distance
Some 4.5 billion kilometres away from the sun, Neptune takes 165 Earth years to complete a single revolution; the average human will never even be able to see Neptune go from one side of the sun to the other - think about that for a minute....
Does it not put into perspective the scale of even just our solar system?
Neptune is so far away that even moving at over 5km per second, it would still take you and perhaps your child's entire lifetimes just to see Neptune through one revolution around the sun.
The scale is staggering....
Using Universe Sandbox to put into perspective how far away Neptune really is - that tiny blue ring that you can just about make out it in the middle is the Earths orbit....

The days are a cold -200 degrees Celsius, and the nights are even colder.
At 4.5 billion kilometres from the sun, it receives radiation from the sun of an intensity 900 times weaker than what the Earth receives.
Not only does this affect the temperature on Neptune, but it also means that the planet reflects very little light, making it too difficult to spot with the naked eye.
Either a reasonably cheap reflecting telescope, or a very expensive refractor would absolutely be necessary for this kind of luminosity and distance (assuming the average person's budget!), but even so you'd be looking at at least a 10 inch aperture to be able to collect enough light from the planet to make out any details.
Still...that's certainly possible to obtain.
Although 3 times smaller than Jupiter, Neptune is still a giant planet with hydrogen and helium making up 99% of its composition - as is the case with most gas giants.
With a diameter of 45,520 km, it's scarcely smaller than Uranus in volume, but is reasonably more massive (Neptune is 17.2 times as massive as Earth, compared to 14.5 for Uranus).
Neptune has 14 moons, the largest and brightest of which is Triton (not to be confused with Saturn's "Titan").
Like the other 3 gas giants, Neptune also has a ring system, albeit of which is far less dense in ice, dust and asteroids than the likes of Saturn.
Scale of the planets... It's hard to make out that Uranus is larger in volume than Neptune here, but I guess you'll just have to trust the various internet sources that say so :) Unless of course you own the necessary instruments to measure them for yourself ?

The discovery of Neptune sparked great controversy in the 19th Century, as its existence was actually predicted by mathematicians before it had even been discovered.
Drawing upon what I've previously mentioned, Neptune is so faint that it's the only planet undetectable by the naked eye.
Since planets were only discovered through the inspection of light sources that can bee seen with the naked eye, discovering Neptune would've proven extremely difficult.
Imagine scanning the universe through a telescope and happening to be in the narrow line of sight of Neptune....
So how come predictions were made about its existence ?
In the 19th Century, astronomers were trying to predict the location of already known planets using mathematics - you have to realise that at this point in time, astronomers didn't have the technology nor the Hubble space telescope to track planets with.
However, there were instruments that could lead to the accurate measurements of quantities like mass and distance.
Using these kind of variables, predictions could be made about the orbits of the planet at question.
In this specific example, the planet at question was Uranus.
Until the end of the 18th century, astronomers had had difficulty in reconciling the observed position of Uranus with its calculated position.
Alexis Bouvard, an astronomer at the Paris observatory, was among the first to notice these irregularities. Along with him, Francois Arago proposed that a massive body (such as a planet) was perturbing the orbit of Uranus, the idea of which quickly achieved currency among fellow astronomers.
An unfortunate event
It should be recognised that Englishman John Coach Adams, along with Frenchman Urban Jean Joseph Le Verrier were among the first to make successful calculations of the proposed whereabouts of this "body", as well as its mass, to allow for its discovery in the constellation of Aquarius.
Cambridge University did not have up-to-date maps of the constellation of Aquarius, and Adams' prediction was dismissed under discrimination of his age by his fellow colleagues - he was deemed too young to be able to make such successful calculations.
On 23 September 1846, the same day that Adams received a letter from Le Verrier that confirmed his predictions were correct, Johann Gotffried Galla discovered the new planet at the Berlin Observatory, marking its position less than 1 degree out from the prediction made by Adams.... Never underestimate your peers...
Right before his own eyes
By a curious chance of history, Neptune had been close to Jupiter in terms of its angle from the perspective of someone on Earth during the winter of 1612-13.
On 28 December 1612, Galileo had been observing Jupiter and the Galilean moons and marked Neptune as a star on his sketches.
As mentioned previously, it must be remembered that Neptune is extremely faint and hence, without sufficient reason to suggest that it's a planet 4.5 billion km away from the sun, it could very well be misunderstood as a faint, distant star, as prescribed by Galileo....
Composition
Elaborating on the composition of Neptune, besides the abundance of hydrogen and helium, methane can also be found in large quantities, of which the planet can owe it's predominantly blue colour to; methane absorbs longer wavelengths of light such as red, while reflecting shorter wavelengths such as blue and purple.
Upon inspection, the most obvious detail of Neptune is the large spot that's very similar to Jupiter's Great Red Spot; given the similarities, it was named the Great Dark Spot.
White stripes can also be seen that appear to surround the spot, which are taken to be Cirrus clouds high up in the atmosphere of the planet, similar to the ones that can be found on Earth. One exception being, however, that the Cirrus clouds here on earth are crystals of frozen water (ice), where as on Neptune they're thought to be crystals of frozen methane.
Being the 8th and final planet in our solar system (to our knowledge - there's a conspiracy around a 9th planet, dubbed planet nine), studying the planet has proven to be much more difficult than say Mars, hence not an awful lot can be said with absolute certainty.
Having said that, Voyager 2 has made remarkable discoveries about the planet, some of which have been mentioned here, but nothing more that I feel is of enough substance to spark much interest here.
I hope you enjoyed this article, and thanks for reading!