"He is nearby."
Translation:Hij is dichtbij.
If you say the sun is 'vlakbij', I'm pretty sure that's relatively vlabij :-) The only difference I can think of is that I would use 'dichtbij' more often for persons and or other things that can move and 'vlakbij' more often for places and or other things that don't move. I don't think one of them is closer. I wouldn't say that that's a rule though. Maybe other Dutch people will disagree.
I dunno, I asked this like a month or two ago and the answer I got from a Dutch person was that one is slightly closer than the other.
But I asked my Dutch friend and she said they mean the same thing. So you may be right, and if you're wrong, then the difference between the two probably doesn't matter that much.
If you use "ligt" for a person, it means that person is lying down. So the sentence would be "He is lying nearby". You can use "ligt" as in "is" or "is located" for things or places that are either in a lying position or are metaphorically lying on the ground (like a country, for example : Frankrijk ligt dichtbij).
Here is a great explanation for this : https://www.duolingo.com/comment/5785064
Litterally, it would mean "He is standing nearby". When it comes to a person, if you don't know in what position they are, you can simply use "is". But if you specify "staan", "zitten", or "liggen", it means you know for sure it what position he was.
So it's different for a person than it is for an inanimate object. For example, if I said "Frankrijk ligt dichtbij", it means "France is close", not "France is lying close".