So my wife and I love to garden but moving up to the Pittsburgh area we have a shorter growing season and our back was fully treed. Last week I had a couple large trees dropped which I am cleaning up. This has created a nice opening in the center of our back but still surrounded by trees, our yard is tiered down so the lower level is south facing. I time lapse yesterday and it seems to get partial sun (overall about 1/2 of the area full sun that moves with the sun) for about 5 hrs, 2 hrs for full sun. This is now with the sun setting a little lower and trees full of leaves.

We have the structure figured out but before we jump in what are the thoughts on the sun? Below is a photo from the timelapse during full sun but you can see the trees below .

I'm relatively new to a greenhouse myself. I suggest you pick up a few books from the library on greenhouses. A lot depends on what you want to use the greenhouse for.

"The Year Around Solar Greenhouse", by Lindsey Shiller has a good chart on regional sun received listed by month. Sounds like your trees will allow more sun in the winter when the leaves are gone.

I know you posted in greenhouses, but as the other reply said, much depends on what you want to accomplish. You have a shorter but not insignificant growing system now.

For extending growing seasons, starting earlier and going longer, temporary tunnels can do that without filling the area with greenhouse.

For just a winter plant refuge and place to start seed for the spring, a small greenhouse is sufficient.

Of course, for growing that requires a controlled environment, a full size greenhouse is appropriate. I need one here for year-round hydroponic growing through weeks of 100+ temperatures and still some freezes and short winter days.

Two hours a day of true full sun is a challenge with some crops. But there's a lot of slack in most light requirements. Tomatoes, for instance, may merely suffer some loss of production in part sun. One thing a greenhouse can do where full sun hours are limited is provide a place where artificial lighting can be brought to bear.

Grow lights are not just for hydroponics. They can be used as adjuncts to natural light in a greenhouse, with the bonus of providing sun equivalent in bleak winters. I have LED strips throughout the greenhouse supporting plants on days of weak sunlight. They are mounted to high and are too few to be the sole light source for growing, but they provide a real boost. They do, though, require a timer to give plants the necessary dark period each night, without which they have limited ability to build with the energies built up during the day.

Grow lights were once sort of expensive, but the increased use of hydroponics for home growing (and not just dope, although that's where a lot of the business is) has brought the Chinese into the grow light business and made effective artificial light growing fairly cheap, and LED lighting is cheap to run.

It's worth looking into, because it can mean home grown lettuce and tomatoes all year. Even things like melons. I'll never again grow lettuce in the ground. A "rain tower" occupies one square foot and can pretty much keep me in salad without sharing with the bugs and such. And a second can keep me in strawberries. (Google RAIN TOWER.)

A greenhouse is a serious hassle. It takes up space you might not have in excess. It's expensive to build, furnish and maintain. It needs tending and cleaning. You have to sacrifice trees for it, and still worry about hale, icicles and falling branches. Keeping it clean is a constant challenge.
(Ours is 10 years old, and needed serious serious repair to the roof. We realized that when a young raccoon wandered into the house one night.)

So, if you intend to undertake such a project, you must have a very good reason to want it. And you need to think about how best to take full advantage of it. What do you desire? What can you grow? How much can you consume?

The first couple of years, we crammed it full of tomatoes, peppers, cucumbers and eggplant, which grew enormous, but didn't produce well. Turns out, you have to invite, even entice, pollinating insects into you greenhouse. Then we had chronic, pernicious white fly infestations. The mail-order ladybugs all died, either en route or shortly after arrival - ants did a better job. Had an outbreak of powdery mildew - and disposing of diseased leaf-litter can be a problem. Cats got in and took advantage of what they saw as indoor plumbing. Had to keep refreshing the soil in the containers; buying earth by the sack. And when it went well, we had so much produce, we couldn't preserve and give it away fast enough.

It's a longish, steepish learning-curve, different for everyone. One thing I can tell you up front, though:
There is no substitute for early, thorough research. Do your math!