Delta and the Bannermen - S24-E3
Corrected entry: Why would a US satellite launch be "history in the making" in 1959? The first American satellite to reach earth orbit (Explorer I) was launched in early 1958.
Corrected entry: In an earlier episode the Doctor states that he is about three hundred years old, in this episode however the pin code on the Rani's door is three digits long and starts with nine, to which the doctor responds "hmm, that's our age." he can't have aged that much as none of his companions aged more than a couple of years.
Correction: Bear in mind that this is a show about time travel. The Doctor has many adventures off-camera as well, and although it's implied otherwise, there's no saying that companions aren't occasionally dropped off and picked up again later, making it entirely possible for decades or centuries to pass for The Doctor between adventures.
Correction: By 1959, the US had only launched five satellites, of which two had failed. A satellite launch would still be novel enough to be "history in the making".