Without studying space, We wouldn't understand time like we do, nor keep it. We also wouldn't understand days and nights, the phases of the moon, or why the stars appear differently every night ( even if the actual change is minute on a day to day basis, they do change.)
The sky has fascinated ( and been feared by) Humans since ancient times, and there have been questions about what's really above us up there. One of the earliest reasons people studies space because it was considered " the playground of the gods" which could explain its distance from mere humans. The sun was often thought to be the most important god, the moon being a close second. An Astronomy timeline ( http://highered.mcgrawhill.com/sites/0072482621/student_view0/astronomy_timeline.html) Illustrates that some of the earliest astrological knowledge was of the phases of the moon and the movement of the sun. Stonehenge, for example, has structures that line up with the sun paths of the equinoxes. most early astronomical observations were of these "heavenly bodies" because they were ( and still are) the biggest objects in the sky and easily observable. Other early records did claim of other objects ( like planets) but they were far and few between since early astronomy ( like other things) was poorly recorded.
Another plausible reason to study space was to possibly understand our own earth and how it would effect our species. Early peoples recorded lunar and solar eclipses but it wasn't until about 480
B.C after taking astrological records from the Babylonians , Thales predicted eclipses. This may not seem so fascinating but to ancient humans didn't understand the concept, the sky going dark at a weird interval might scare people, and make them think they were being punished by the gods. Once Thales was able to predict some eclipses it made us seem like we were "more in control of" space, not that we really were. ( you can read the rest of the article here :http://abyss.uoregon.edu/~js/ast121/lectures/lec02.html ) The article discusses the formation of several Heliocentric ( Sun revolving) models of the solar system and Geocentric ( Earth Centering) models as well. and in learning out position as an orbiting planet of the sun and not vice versa. we could understand our earth and it's proximity to other astronomical objects as well.
Time was another important factor in why we study space. At some point we needed a way to know how long a day way and how id we spate that day up and split those days into much longer months. It started with the sun's path but slowly it evolved. the Original roman calendar was based solely on the lunar months made up with 10 solar months. Well several months got added ( at one point there was a month that showed up every two years after February) and things went that way until Julius Caesar got told to follow the solar calendar which was accurately timed at 365 days and 6 hours. This was the beginning of our modern calendar time. Our Watches also run on solar time, not sidereal time which is the true movement of the earth. ( Here is a comparison of Solar days and Sidereal time : http://www.universetoday.com/14700/how-long-is-a-day-on-earth/ )
That is all ancient history though. Yet we still study the cosmos, apparently unappeasable with without knowing what's around us and what's Really out there. Every year there are seemingly endless new studies and discoveries that were unknown to us before. We may not know why they are up there, but were going to try pretty hard to understand what's up in the cosmos.
EDIT: Thanks to a helpful comment by Mrs. Herrold, it seems I am missing part of the blog... Why do we continue to study space? I believe its to try and understand what is around us in the universe in our solar system, our galaxy, our side of the universe etc., as most humans have a lust for answers and knowledge. We search to see if we can break down complicated mysteries into easy to digest terms that we already can comprehend. We are all made of particles of the universe and maybe we can learn where we come from, and what came before us, and maybe what will happen after. To quote a favorite novel The Fault in Our Stars "There was a time before consciousness and there will be a time after." We're just trying to comprehend what we can in our little blip in time.