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Moving through space in The Lost Fleet universe, that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time, when inside a solar system or in jump space between them.

In our case we're talking about the Fleet consisting of hundreds of ships, which are military designs, meaning highly maneuverable and fast units, heavily armed and armored in some cases, which means they will have a lot of mass. Propelling that mass requires a lot of energy. Energy generation requires fuel.

In order to propel such a starship to, say, 0.2c requires significant energy and the higher the acceleration the more fuel it requires.

But in space there is nothing to slow that vessel down. So, what it has to do to change direction? Or better yet: turn around left and down?

Exactly: basically exactly the same thing it did to attain the speed and direction along the plotted course in the first place, and twice that if it is "3-D" turn-around.

But if we want that ship to not be constantly subject to stresses of high-g maneuvering (and it is said in the books that any ship can basically loose propulsion under maximum load), we have to do low-g maneuvering.

Which literally means that instead of turns of radius of hundreds of kilometers, there will be turns with radius of hundreds of thousands of kilometers... Which will look on the plots like lines "curved in a graceful arc"...

Moving through space in The Lost Fleet universe, that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time, when inside a solar system or in jump space between them.

In our case we're talking about the Fleet consisting of hundreds of ships, which are military designs, meaning highly maneuverable and fast units, heavily armed and armored in some cases, which means they will have a lot of mass. Propelling that mass requires a lot of energy. Energy generation requires fuel.

In order to propel such a starship to, say, 0.2c requires significant energy and the higher the acceleration the more fuel it requires.

But in space there is nothing to slow that vessel down. So, what it has to do to change direction? Or better yet: turn around left and down?

Exactly: basically exactly the same thing it did to attain the speed and direction along the plotted course in the first place, and twice that if it is "3-D" turn-around.

But if we want that ship to not be constantly subject to stresses of high-g maneuvering (and it is said in the books that any ship can basically loose propulsion under maximum load), we have to do low-g maneuvering.

Which literally means that instead of turns of radius of hundreds of kilometers, there will be turns with radius of hundreds of thousands of kilometers... Which will look on the plots like lines "curved in a graceful arc"...

So, bottom line is still the answer I gave initially: fuel conservation. Also to avoid unnecessary engineering casualties due to stress of constantly travelling at maximum power. So to also conserve spare parts, to avoid delays and more fuel consumption to slow down in order to keep formation. And not to leave anyone behind.

Since Fleet is moving through star system that is not empty - if for no other reason than the big star in the middle - and is recovering from a fight and low on fuel, was travelling deeper into system for some time before selecting exit jump point, it's obvious why its path is gracefully curved: conserve fuel.

Moving through space that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time. In addition, jump points are on the same plane of ecliptic. Which means that unless entry and exit jump points are next to each other or at least reasonably close and on the same side of the sun, the course between them will never be straight line. This is because the Fleet needs to steer clear of the sun to some degree.

So the path through the system in question needs to be calculated taking all suns, planets, moons into account, so that all of them will be at a distance that will not impact the movement. This allows for least-burn course correction along this path, take advantage of gravitational fields of system's bodies and so on. For example, 5 second burn at 10% of power, on hour 2 of day 0 of travel in-system can result in passing a gas giant with light-hours to spare instead of light second, which may require to use of propulsion for 1 minute at full power then.

As a side note - on Earth, even when ships go along the shortest line connecting two points of the travel, it's not a straight line and it's also not straight in 3-d due to the curvature of the Earth and insufficient precision of navigational/guidance systems.

You are making assumptions which I do not see as reasonable - for example, sun WILL exert gravitational pull on the fleet regardless of it's speed or distance from that sun. Course calculation takes into account and, for example, if the fleet will bypass the sun on it's "left side", it will make greater turn to the right to compensate for that. In this specific instance the Fleet came to this star system right after combat, it then proceed to salvage supplies without breaking formation. This was done for several reasons: to optimize rearming and refuelling, cross-transfers of personnel and supplies and in order to not weaken the Fleet in case of ambush or pursuit. Also, to avoid giving away their destination jump point (but also due to indecision).

Moving through space in The Lost Fleet universe, that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time, when inside a solar system or in jump space between them.

In our case we're talking about the Fleet consisting of hundreds of ships, which are military designs, meaning highly maneuverable and fast units, heavily armed and armored in some cases, which means they will have a lot of mass. Propelling that mass requires a lot of energy. Energy generation requires fuel.

In order to propel such a starship to, say, 0.2c requires significant energy and the higher the acceleration the more fuel it requires.

But in space there is nothing to slow that vessel down. So, what it has to do to change direction? Or better yet: turn around left and down?

Exactly: basically exactly the same thing it did to attain the speed and direction along the plotted course in the first place, and twice that if it is "3-D" turn-around.

But if we want that ship to not be constantly subject to stresses of high-g maneuvering (and it is said in the books that any ship can basically loose propulsion under maximum load), we have to do low-g maneuvering.

Which literally means that instead of turns of radius of hundreds of kilometers, there will be turns with radius of hundreds of thousands of kilometers... Which will look on the plots like lines "curved in a graceful arc"...

Since Fleet is moving through star system that is not empty - if for no other reason than the big star in the middle - and is recovering from a fight and low on fuel, was travelling deeper into system for some time before selecting exit jump point, it's obvious why its path is gracefully curved: conserve fuel.

Moving through space that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time. In addition, jump points are on the same plane of ecliptic. Which means that unless entry and exit jump points are next to each other or at least reasonably close and on the same side of the sun, the course between them will never be straight line. This is because the Fleet needs to steer clear of the sun to some degree.

So the path through the system in question needs to be calculated taking all suns, planets, moons into account, so that all of them will be at a distance that will not impact the movement. This allows for least-burn course correction along this path, take advantage of gravitational fields of system's bodies and so on. For example, 5 second burn at 10% of power, on hour 2 of day 0 of travel in-system can result in passing a gas giant with light-hours to spare instead of light second, which may require to use of propulsion for 1 minute at full power then.

As a side note - on Earth, even when ships go along the shortest line connecting two points of the travel, it's not a straight line and it's also not straight in 3-d due to the curvature of the Earth and insufficient precision of navigational/guidance systems.

You are making assumptions which I do not see as reasonable - for example, sun WILL exert gravitational pull on the fleet regardless of it's speed or distance from that sun. Course calculation takes into account and, for example, if the fleet will bypass the sun on it's "left side", it will make greater turn to the right to compensate for that.

Since Fleet is moving through star system that is not empty - if for no other reason than the big star in the middle - and is recovering from a fight and low on fuel, was travelling deeper into system for some time before selecting exit jump point, it's obvious why its path is gracefully curved: conserve fuel.

Moving through space that is mostly empty, and where non-empty spots would be suns, planets, moons etc., involves great distances and days of time. In addition, jump points are on the same plane of ecliptic. Which means that unless entry and exit jump points are next to each other or at least reasonably close and on the same side of the sun, the course between them will never be straight line. This is because the Fleet needs to steer clear of the sun to some degree.

So the path through the system in question needs to be calculated taking all suns, planets, moons into account, so that all of them will be at a distance that will not impact the movement. This allows for least-burn course correction along this path, take advantage of gravitational fields of system's bodies and so on. For example, 5 second burn at 10% of power, on hour 2 of day 0 of travel in-system can result in passing a gas giant with light-hours to spare instead of light second, which may require to use of propulsion for 1 minute at full power then.

As a side note - on Earth, even when ships go along the shortest line connecting two points of the travel, it's not a straight line and it's also not straight in 3-d due to the curvature of the Earth and insufficient precision of navigational/guidance systems.

You are making assumptions which I do not see as reasonable - for example, sun WILL exert gravitational pull on the fleet regardless of it's speed or distance from that sun. Course calculation takes into account and, for example, if the fleet will bypass the sun on it's "left side", it will make greater turn to the right to compensate for that. In this specific instance the Fleet came to this star system right after combat, it then proceed to salvage supplies without breaking formation. This was done for several reasons: to optimize rearming and refuelling, cross-transfers of personnel and supplies and in order to not weaken the Fleet in case of ambush or pursuit. Also, to avoid giving away their destination jump point (but also due to indecision).