You don't draw cards until the end of your turn. Gravity is resolved when you play the card. I imagine you must take the free matter for Gravity before you draw.
There, you see... that's exactly why I asked the question!
Your reply makes perfect sense now that I think about it. I had a feeling that there actually might be a specified order to the sequence. Plus, your reply forced me to go back to the rulebook, to see where I may've missed what you wrote. And sure enough, its right there on page 5!
The Turn Summary on page 5 does indeed show that playing a card and drawing a card are two distinctive steps, performed in that order. I never revisited that section after my initial reading of the rulebook and instead focused on the rest of the rulebook (starting on page 6) when playing the game.
Thanks for the reply!