If she had an ultrasound in her sixth week, it could be spot-on for dating pregnancy or only off by possibly 1 day. But at nearly 9 weeks, there is a margin for error in using an ultrasound to date pregnancy, as the doctor said. If she had had the ultrasound at 6 weeks 0 days, given the estimated due date of January 19, the most probable date of conception would be April 28. But since it was an eighth-week ultrasound and not a sixth-week ultrasound, the margin for error readily covers dates as far back as April 22. And don't forget, your sperm can live up to 5 or 6 days in her system. You could have sex on April 25 and she could conceive on April 30 from that sex. So I don't really see why you are acting like this. Do you have a real reason to mistrust her? You can ask for a DNA test when the baby is born, but it will insult her a lot to do so, meaning, you had better be super-tactful and very careful in the way you do it. If she is going to expect child support, you could have a quiet word with your attorney and ask him to request it and make it sound like it is necessary to give to the court.
Thank you Annie for your concise analysis. I tried as hard as one could muster to avoid 'insulting' my girlfriend. I merely questioned why the doctor said 8 weeks 6 days whilst, according to my calculations, it was 7 weeks on the dot. My own, obviously flawed, chart indicated that it would only be 8 weeks on 22 June - 22 April to 22 June. She indicated to the doctor that she does not remember the date of her last period. So the doctor deciphered the likely date of conception purely from reading the ultrasound device (or maybe from other factors). He estimated the date of delivery as 19 January 2016.
Incidentally, did the doctor give her a due date? You can count back 266 days on a calendar from the estimated due date and get an estimate conception date, or use a conception calculator online. From you saying 8 weeks 6 days on June 15, I get conception as being on April 28, which makes plenty of sense given you having sex from April 22 to 25. (Not only is there the margin for error mentioned by the doctor but also, sperm can live up to 5 or 6 days in a woman's reproductive tract.) It just all adds up. I hope you have not said anything insulting to your girlfriend.
Tumi, it all adds up to you being the dad. Doctors count pregnancy as beginning on the first day of the last period, not on the presumed day of conception. Your girlfriend's doctor is saying that computed from average cycle lengths of lots of women, her last period began 8 weeks 6 days ago. That would then be logical that sex around April 27 would produce a pregnancy. Sperm can live in a woman's body for several days after sex. You are exactly in the right time frame.
If it helps, here is how I have explained the difference between how a doctor times pregnancy and how the average person might time pregnancy, in past posts.
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All medical counts of pregnancy (the number like 6 weeks 3 days) begin on the first day of the last period you had before getting pregnant. If a doctor says to a woman, "Congratulations, you are 8 weeks pregnant!" he means 8 weeks since her last period began, or about 6 weeks since conception. The count is done this way because the period is a big, obvious signal, the only signal they had in the days before ultrasounds, not because the doctor thinks the woman is pregnant on day 1 of her cycle. (She's not pregnant then, she is having a period!) That's why pregnancy, which takes 38 weeks, is counted as being 40 weeks long. They add a spare two weeks at the front to count back to the presumed first day of the last period.