What is a ‘launch window’?

NASA announced that coming Space Shuttle launch window would run from May 12 to June 3, 2005. So, what is a ‘launch window’?
A launch window is a particular period of time in which it will be easier to place the spacecraft in the orbit necessary to perform its intended function.
If the spacecraft intends to rendezvous with another spacecraft, a planet, or other point in space, the launch must be carefully timed so that the orbits overlap at some point in the future. If the weather is bad or a malfunction occurs during a launch window, the mission must be postponed until the next launch window appropriate for the flight. If a satellite were launched at the wrong time of the day in perfect weather, the satellite could end up in an orbit that would not pass over any of its intended users.

If we are going to send a mission to a planet why not just launch the rocket at any time, find where The planet is in the sky, point the rocket at it and travel there?

Imagine the Solar System as an athletics race track. If you were watching the 400 metres race from the centre of the track and wanted to intercept one of the runners taking part, one way would be to simply chase the runner you wish to stop. If you were fast enough, you might eventually catch up but only after expending a lot of energy and travelling a long way.
A much better way to intercept your athlete is simply to walk across the centre to the other side of the circular track. It is a much shorter distance and you use a lot less energy and time getting there.
You calculate your walk so that you arrive at the other side of the track at the same time as they do. Too early and you are waiting around for them. Too late and you have missed them completely – you’d have to wait one lap until they came around again.

In spaceflight, straight-line paths do not exist for the same reason. All planets move in long, curved paths around the Sun that take the shape of circular and elliptical orbits. In order to reach the targeted planet, the spacecraft must leave Earth and then travel in an elliptical orbit around the Sun that will eventually intersect the orbit of the planet.
Calculating the launch window for the planetary mission involved timing the launch to allow the spacecraft and the intented planet to arrive at the same point in space at the same time.
With the Space Shuttle, an extremely important factor in choosing the launch window is the need to bring down the astronauts safely if something goes wrong. The astronauts must be able to reach a safe landing area where rescue personnel can be standing by. One important safety constraint is to have a daylit Trans-Atlantic Landing (TAL) site. If the Space Shuttle were to have engine trouble and have to land before it gets to space, it would use a TAL site.
For example, the MIR rendezvous mission (STS-71), had only a five minute launch window. Another example would be a Shuttle mission deploying a satellite destined for another planet. Because the Earth and the other planet have to be in a certain alignment to accomplish the journey with the engine and the amount of fuel on board, the mission might have a launch window of only a few days in a specific month.

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