Once a space vehicle has been sent into space and has reached a certain speed will it maintain that speed with no further thrust?
Also if it will maintain that speed can storing solar energy be used to add additional thrust and continue to accelerate the vehicle slowly over a long period of time?
Yes. As long as there are no forces acting on the vehicle it will remain at its current speed “forever”. (Even in deep space there are minute forces working on it, gravitational pulls and a tiny amount of drag,but these will take eons to have any impact, as long as the vehicle stays clear of the gravity wells of planets, stars and such).
And yes, one could harness solar energy to power some sort of engine (or even use sail to ride the solar winds), but of course, as the vehicle moves away from the sun, this would rapidly become less and less effective.
Could a “solar lazer relay” system possible be set up or would it loose too much energy as it moved away?
Kind of. Newton’s First Law: an object remains at rest or moving with a constant velocity unless a net force acts upon it. So in ‘deep space’, yes. In a gravitational field, not exactly. But nearly, if the field is weak. So for example, to a reasonable approximation, all the probes we shoot off to other planets travel at constant speed once we’ve sent them on their way. Of course the Sun is still pulling them, but only the eggheads at NASA need to account for that.
I expect so. I dunno about storing the energy, but solar sails work by being pushed by sunlight. As you surmise, it’s a tiny amount of acceleration that needs to act for quite some time.
Not exactly. Its speed and trajectory is influenced by gravity. If you send a probe away from Earth with speed less than the escape velocity (about 11.3 km/second or 25,300 mph), its speed will gradually drop before it starts falling back to the earth. Depending on how much “sideways” speed it has, it may impact the earth, or it may remain in orbit around earth.
If you send it on an escape trajectory, it will leave the earth and essentially act like an asteroid or comet - i.e. in its own orbit around the sun. It may enter an elliptical orbit around the sun, or it may be in an escape trajectory - it will continue to slow down, but eventually make it out of the solar system.
You can’t accelerate with just pure energy*. In order to create thrust, you need to heat up or accelerate some propellant and shoot it out the back of the spacecraft. Ion thrusters are used on some interplanetary probes that need to do a lot of course corrections along the way (e.g. visiting multiple asteroids).
*Actually that’s not strictly true - since photons have momentum, in theory you could propel yourself by just using a light source. But it’s an extremely inefficient system.
“Launching lasers” are a standard in science fiction, and could certainly work in reality. A space probe would extend large reflective sails, and an earth-based laser would be aimed at them. The “light pressure” (yes, light really does exert force on the objects it shines on) would cause the sails, and thus the probe, to accelerate away.
There are even clever (hypothetical) designs involving detachable mirrored sails to allow the spacecraft to decelerate when it arrives at its destination.
Maybe some day, we’ll see experimental prototypes.