How does the Doctor's aging work?

Question

How exactly does The Doctor's aging work? It appears to be all over the place. From revived Doctor Who alone:

• In The Sound of Drums, The Doctor is aged 100 years and becomes an old man.
• In The Last of The Time Lords, The Doctor is aged a further 900 years and becomes a tiny Dobby-like creature.
• In The Impossible Astronaut, Amy and Rory see a 200 years older Doctor than the one they last saw and he looks exactly the same as the one they saw earlier who was 200 years younger.
• In The Time of the Doctor, The Doctor ages for 900 years and looks like a normal, older human.*

And this isn't even counting all the Classic DW aging shenanigans, so what's up?

*I know that was asked here but none of the answers really worked for me.

Answer 1

I doubt you'll get much more than speculation on this one. There's far too much timey-wimey bullshitty-wullshit in Doctor Who for it all to be reasonably said. That said, here's some speculation :-)

I'm going to quote a block of text from the wikia (emphasis mine):

Even without regeneration, Gallifreyans had considerable lifespans. Within one regeneration, Gallifreyans could live for hundreds of years, yet look much younger than a human of equivalent age. When artificially aged 500 years, the Fourth Doctor looked like an elderly human (The Leisure Hive). During his eighth incarnation, the Doctor spent over a century trapped on Earth and never seemed to physically age during that time. In his eleventh incarnation, the Doctor looked essentially the same for two centuries, (The Impossible Astronaut) though at least three more centuries caused him to age somewhat and six more centuries of further time caused him to age into a very old man, near death from old age. (The Time of the Doctor)

However, Gallifreyan children grew at about the same rate as humans of the same age. (The Sound of Drums) After this point, ageing would slow, with the Gallifreyan looking like a teenager for decades. The Tenth Doctor referred to himself at ninety years old as being "just a kid". (The Stolen Earth)

The Second Doctor once stated that, barring accidents, his people could "live forever". (The War Games) The Doctor once said that he considered himself at approaching 750 to be middle-aged. (Pyramids of Mars) One Time Lord, Quences, was killed when he was over 7,000 years old. Professor Chronotis suffered from senility when over 12,000 years old, and the Eleventh Doctor showed some signs of the same on the brink of his thirteenth and supposedly final death at "over 2000" years old. (The Time of the Doctor, Deep Breath)

From this it sounds like ageing works differently according to a Gallifreyan's position within their lifespan. We know for sure that when they're young they age like humans, and later on their ageing slows. The evidence in your question suggests they age more quickly towards the end of their life (or maybe towards the end of each regeneration, if they regenerate due to old age?) as well as the start. This would explain why the Doctor didn't age in The Impossible Astronaut but did in other episodes, each time shortly before regeneration.

Answer 2

In The Sound of Drums, The Doctor is aged 100 years and becomes an old man.

In The Last of The Time Lords, The Doctor is aged a further 900 years and becomes a tiny Dobby-like creature.

The 100 and 900 year figures were directly from The Master. There is no context there to make us think that he is speaking in terms of the effects of literal, terrestrial years on a Time Lord. Given his audience, he may have been converting to relative human aging on the fly.

In The Impossible Astronaut, Amy and Rory see a 200 years older Doctor than the one they last saw and he looks exactly the same as the one they saw earlier who was 200 years younger.

In The Time of the Doctor, The Doctor aged 300 years and became very old looking.

This is consistent with what we saw of The First Doctor back in the '60s. After his regeneration, The Second Doctor gave his age as something around 450 years old. While his regeneration may have been triggered in part by the energy draining effects of the Cyber-planet Mondas, old age certainly played a part as well; he was quite frail, especially at the end, and conceded that his body had "worn thin". This gives us a ballpark estimate of how long an active Time Lord body can be expected to serve. What hints were dropped of The War Doctor's age at regeneration match with this as well. As 1, War, and 11 are the only incarnations of The Doctor to regenerate due in any large part to old age, these incidents form a remarkably consistent picture by Doctor Who standards.