On what day did Ganon awaken in Breath of the Wild?
(Or 'How much time does it take, logistically, to go from Sanidin Park to Mount Lanayru and then back to Lanayru Promenade?')
In memory #14 Zelda informs Link that the following day it's her birthday and that she will then make her way to the Spring of Wisdom. From the position of the sun and the direction of the shadows, we can tell that memory #14 happens at dawn. According to the description of the memory, they are returning from a field survey.
In memory #15, when Zelda and Link meet the champions at the East Gate of Lanayru promenade, after having returned from the spring, Ganon Awakens.
But how much time passed between the two memories? (Assuming they mean to reach the mountain as soon as possible or if we are just interested in knowing the earliest they could have taken to reach it.)
It depends of the path they have taken. There are two probable options:
Returning to the Castle, then heading to the mountain (purple + yellow in the map);
Going directly to the mountain (red + yellow in the map).
To see how much time these paths take, I've recreated their trip by travelling along the main road, riding the descendant of Zelda's horse. I've opted for trotting, the second slowest speed, because realistically a horse shouldn't be abused and in memory #14 they ride even slower.
RETURNING TO THE CASTLE, THEN HEADING TO THE MOUNTAIN - PATH #1
Starting the journey at about 5:00 from Sanidin Park, you can arrive at Castle Town at about 14:30. It should take a little more to arrive to the castle itself, but I wasn't able to ride there due to the high number of guardians. We should add half an hour for lunch, likely at the village by Carok bridge, bringing the hour of arrival at 15:00.
Regardless, if they have not taken the direct shorter route but decided to make a stop at the castle, Link and Zelda do not mean to leave for Mount Lanayru until the next day.
The next day, if they leave Castle Town at 6:00, considering that they have left the Castle itself even earlier, they can arrive to Dueling Peaks Stable at about 23:00. The first couple of hours are very approximative, as the guardians hindered me and, when I killed them all, they bloodmooned. We should add half an hour for lunch, likely on the road or, if late a lunch, at Gatepost Town, and half an hour for dinner, likely on the road. After counting the breaks, it would be already 00:00, too late to travel further, so they would likely spend the night at the stable.
GOING DIRECTLY TO THE MOUNTAIN - PATH #2
Starting at about 5:00 from Sanidin Park, you can arrive at Dueling Peaks Stable at about 21:00. We should add half an hour for lunch, likely at Gatepost Town, and half an hour for dinner at the stable. After counting the breaks, it would be already 22:00, too late to travel further, so they would likely spend the night at the stable.
From this point onward, both paths are at the same daily time, but the first path happens a day later.
Starting at about 5:00 from the stable, you can arrive at Kakariko Village by 9:30, where they would probably stop for half an hour.
From there, they would proceed off the main road to the Lanayru Promenade. They would arrive at the East Gate at about 16:00. We should add half an hour for lunch on the promenade, bringing the time of arrival at 16:30.
Since in memory #15 Link and Zelda don't have their horses after the East Gate in Naydra Snowfield, from here I proceeded on foot, walking at the same pace they usually walk when they travel in memories.
Following the path mostly hidden by the snow, it takes an eternity to go anywhere at this pace. At 21:30, I was just at the end of Naydra Snowfield. Adding an half an hour for dinner, it brings the hour of arrival at 22:00, so I believe this is where they would have camped.
The next day, starting at about 5:00 from the end of Naydra Snowfield, you can arrive at the Spring of Wisdom at about 17:00.
We should add at least an hour and a half for lunch on the road and frequent breaks, since the road is uphill. Also adding half an hour for dinner, bringing the time to 19:00. It is reasonable to presume that for the night they camped at the spring.
Given the direction of the shadows and the position of the moon, the prayer in memory #13 happens at about 00:00, so it is more likely than not that Zelda makes her prayer between sunset and dawn.
I haven't actually walked all the way back to the East Gate of Lanayru Promenade, but assumed it still takes about a day and a half, which is also in agreement with them arriving at the gate to meet with the champions at sunset in memory #15, considering the direction shadows and the position of the sun in the memory.
That's when Ganon returns!
So the two paths take this long:
Returning to the Castle, then heading to the mountain:
DAY -1: Returning at the Castle;
DAY 0 (Zelda's birthday): Travelling from the Castle to Dueling Peaks Stable;
DAY +1: Travelling from Dueling Peaks Stable to the end of Naydra Snowfield;
DAY +2: Travelling from the end of Naydra Snowfield to the Spring of Wisdom;
DAY +3: Travelling from the Spring of Wisdom up to some point down the path:
DAY +4: Resuming the travel up to the East Gate of Laynaru Promenade. GANON RETURNS!
Going directly to the mountain.
DAY -1: Travelling from the Sanidin Park to Dueling Peaks Stable;
DAY 0 (Zelda's birthday): Travelling from Dueling Peaks Stable to the end of Naydra Snowfield;
DAY +1: Travelling from the end Naydra Snowfield to the Spring of Wisdom;
DAY +2: Travelling from the Spring of Wisdom up to some point down the path:
DAY +3: Resuming the travel up to the East Gate of Laynaru Promenade. GANON RETURNS!
Personally I think the path in which they initially return to the castle is the most sensible, because:
The description of memory #14 says they are 'returning', which strongly implies returning to the castle.
Zelda says she will make her way to the spring after the following day.
It would be unrealistic for Link to be informed of the journey just as they are about to begin it.
Therefore I believe Ganon returned 4 days after Zelda's birthday at the earliest and that it is not possible for him to have returned on the day of her birthday.
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