Maybe I blinked at the wrong moment and missed something, and I don't have a copy of the ep to hand... but it didn't seem to me that her being found dead from a self-inflicted gunshot in a London apartment would have the same sort of inspirational effect as her being martyred in a tragically heroic mission to Mars.
The alternate endings that occurred to me while the end credits were still rolling were:
1. The three he rescues become the next companions. 2. He takes them to some place where they'll be safe, but won't screw up the timeline. 2a. (my favourite) He takes them to the extrasolar planet where Brooke's grand-daughter will land, re-uniting her with her family. 3. Brooke realizes that leaving her corpse for her family to find is not going to inspire anyone to explore the universe - quite the contrary. Instead, she arranges for herself, Mia and Yuri to disappear (or, alternatively, shoots them and disposes of their bodies before committing suicide in a manner that won't leave an identifiable corpse). 3a. Realizing that the Doctor has gone power-mad, she shoots him first, to prevent him fouling up time any further.
4 (which I thought of later). Not exactly a changed ending: something earlier in the episode to indicate that Brooke needed to leave Earth for reasons of her own, and her despair at being returned there led her to commit suicide. (One possibility was that her heart was no longer able to cope with 1 gravity: I know this is asking a bit much of scientifically semi-literate tv, but I was also annoyed that everyone adapted instantly to Earth gravity after a year on Mars. And don't try to tell me they'd bother putting artificial gravity in the colony.) 5 (which I thought of just now). She uses the gun to force the Doctor, Yuri and Mia back into the TARDIS, and makes the Doctor think for a moment about the consequences of his actions.
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The alternate endings that occurred to me while the end credits were still rolling were:
1. The three he rescues become the next companions.
2. He takes them to some place where they'll be safe, but won't screw up the timeline.
2a. (my favourite) He takes them to the extrasolar planet where Brooke's grand-daughter will land, re-uniting her with her family.
3. Brooke realizes that leaving her corpse for her family to find is not going to inspire anyone to explore the universe - quite the contrary. Instead, she arranges for herself, Mia and Yuri to disappear (or, alternatively, shoots them and disposes of their bodies before committing suicide in a manner that won't leave an identifiable corpse).
3a. Realizing that the Doctor has gone power-mad, she shoots him first, to prevent him fouling up time any further.
4 (which I thought of later). Not exactly a changed ending: something earlier in the episode to indicate that Brooke needed to leave Earth for reasons of her own, and her despair at being returned there led her to commit suicide. (One possibility was that her heart was no longer able to cope with 1 gravity: I know this is asking a bit much of scientifically semi-literate tv, but I was also annoyed that everyone adapted instantly to Earth gravity after a year on Mars. And don't try to tell me they'd bother putting artificial gravity in the colony.)
5 (which I thought of just now). She uses the gun to force the Doctor, Yuri and Mia back into the TARDIS, and makes the Doctor think for a moment about the consequences of his actions.