Unlike most sci-fi stories set in this time period, faster than light travel does not exist. However, advances in propulsion technology have led to cheaper and cheaper fuels, and cheaper to operate propellant systems. It has now reached a state in which ships can easily travel at 1G of thrust for long lengths of time; in fact they can travel at much above 1G, but going above 1G causes intense discomfort and often injury for the passengers and crew who are forced to live in high gravity conditions for the duration of the flight.
An extremely useful tool for calculating travel times can be found here http://www.transhuman.talktalk.net/iw/TravTime.htm
Wolfram Alpha can calculate the distance between any two bodies at any date in time
Celestia is also useful for a visual representation at any given date
Artificial gravity in the way that Star Trek, Star Wars, Battlestar Galactica, etc portray it is also not possible in this campaign universe. Instead, realistic methods of generating artificial gravity are used by spacecraft. Three forms are in widespread use:
Most space stations use Spin Rings spun at a rate to generate the desired gravity for those living inside the rings.
Ships on the other hand usually just keep a constant acceleration of whatever G is desired, thus simulating gravity during their trip. Any individual who’s spend any amount of time on a spacecraft will have experienced Zero G conditions a great deal, whenever the ship is engaging in docking or non-travel maneuvers.
Simulated gravity using magnetism is also employed in some ships and space stations. By lining the floors and interiors of the structure with powerable magnets and a computerize system, and pairing this with similarly powered magnetic clothing for those moving through the structure a computer system can power the magnets in such a way to allow movement in a way similar to that in the desired gravity. This feels and acts noticeably different than either of the other two methods since really you’re just stuck to the floor, but it is sometimes used in situations where the other methods are not viable.
Numerous types of weaponry exist in the 24th century, including traditional slug throwing weapons which are still in widespread use, explosive chemical weaponry, and energy based laser weaponry.
Medical Science has made huge strides in the 24th century, discovering cures and treatments for the vast majority of the world’s diseases and disorders. Injury treatments have also experienced great advancements, with lost organs and limbs being able to be regrown and re-attached. Knowledge of the human brain and nervous systems have allowed cybernetic systems to be installed in those who desire them, and modification of a person’s very genes is commonplace, both before and after birth.
One type of medical science that is quite important is in the field of aging. Due to the ability to ability to regrow and replace organs, physical damage from aging can be arrested in those who have the means to pay for treatments. However, the human mind has not yet evolved to be able to properly deal with such extended lifespans, so those who have continued their life greatly over the natural threshold often experience strange and debilitating neural symptoms.
Robotics and Artificial Intelligence
Robotic technology continued to advance as humanity developed higher and higher levels of technological mastery, culminating in 2197 when the first fully conscious AI was believed to have been developed. The AI consisted of a synthetic neural system that functioned identically to a human brain.
However, the moral and legal implications of creating a mind that was human in every way, but was still manufactured like a machine proved too much for humanity to handle. An agreement was reached and synthetic brains were made illegal, thus effectively halting the advancement of AI development. AI computer programs which closely mimic the complexity of a sapient mind are now commonplace, and many of them are advanced enough as to easily pass Turing tests, however the fundamental technology means that they are not quite conscious in the same way as a human brain, and thus no human rights issues may apply to them.