On an infinite plane, the Prime Star has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their eponymous directions.

The Star Guardian at the center wants to reunite the four Stars back into the Prime Star again, which can only be achieved if the four Stars meet at a single point in spacetime. Furthermore:

1. The Star Guardian moves at a constant speed of g, in any direction she wants.
2. She is only able to take one Star with her in her movement.
3. Once left alone, the four Stars always travel in their eponymous directions at speed 1.
4. If only two or three Stars meet, they will just pass through each other without any interaction.

Suppose now 1 unit of time has passed so each Star is at distance 1 from the Guardian, what is the minimum value of g for her to be able to reunite the Stars in finite time? How long will it take her in that mission?

On an infinite plane, the Prime Star has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their eponymous directions.

The Star Guardian at the center wants to reunite the four Stars back into the Prime Star again, which can only be achieved if the four Stars meet at a single point in spacetime. Furthermore:

1. The Star Guardian moves at a constant speed of $g$, in any direction she wants.
2. She is only able to take one Star with her in her movement.
3. Once left alone, the four Stars always travel in their eponymous directions at speed 1.
4. If only two or three Stars meet, they will just pass through each other without any interaction.

Suppose now 1 unit of time has passed so each Star is at distance 1 from the Guardian, what is the minimum value of $g$ for her to be able to reunite the Stars in finite time? How long will it take her in that mission?

Update: it is possible that there exists $g^*$, such that the Guardian is able to complete her mission for any $g\gt g^*$, but not for $g\leq g^*$. If this is the case, identify this $g^*$.

On an infinite plane, the Prime Star at has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their eponymous directions.

The Star Guardian at the center wants to reunite the four Stars back into the Prime Star again, which can only be achieved if the four Stars meet at a single point in spacetime. Furthermore:

1. The Star Guardian moves at a constant speed of g, in any direction she wants.
2. She is only able to take one Star with her in her movement.
3. Once left alone, the four Stars always travel in their eponymous directions at speed 1.
4. If only two or three Stars meet, they will just pass over each other without any interaction.

Suppose now 1 unit of time has passed so each Star is at distance 1 from the Guardian, what is the minimum value of g for her to be able to reunite the Stars in finite time? How long will it take her in that mission?

On an infinite plane, the Prime Star has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their eponymous directions.

The Star Guardian at the center wants to reunite the four Stars back into the Prime Star again, which can only be achieved if the four Stars meet at a single point in spacetime. Furthermore:

1. The Star Guardian moves at a constant speed of g, in any direction she wants.
2. She is only able to take one Star with her in her movement.
3. Once left alone, the four Stars always travel in their eponymous directions at speed 1.
4. If only two or three Stars meet, they will just pass through each other without any interaction.

Suppose now 1 unit of time has passed so each Star is at distance 1 from the Guardian, what is the minimum value of g for her to be able to reunite the Stars in finite time? How long will it take her in that mission?