The 502 calories you have calculated is the number of calories you would be allowed to eat in 1 day, if you wanted 3 pounds in a week. Not much is it??? The 1500 calorie number is the number of excess calories you need to burn every day, not consume.
For most women 1 to 2 pounds lost is about all your body can accomplish in a week. For one thing, 500 calories is really not enough food to keep you functioning without going into serious mental, emotional, and physical slump. Secondly, most bodies will go into a metabolic protective mode where the body just won't release the energy reserves in fat because the body is trying to protect you from starvation. (Thousands of years of adaptation has taught our bodies all sorts of survival techniques, and this is one of them).
So, you might want to run the calculations again for 1 or 2 pounds. A 500 calorie deficit (1 pound per week) would put your daily consumption at 1500 calories, which if you are just starting out will be challenging enough. 1000 calories a day will give you an approximately 2 lbs/week loss. But as you will surely see from reading the posts, 1000 calories requires very careful planning. A couple of crackers, or handful of nuts can put you way over.
Sorry to be the barer of bad news, but losing weight is not for sissies! It takes dedication and patience. But it is totally do-able, as you will surely see by the posts from all these folks who have suceeded.
Post back if you have other questions. There is tons of experience and knowledge here.