Then'd we'd have to consider the gravitational pull of the sun, as well. What messy business! -------------------------------------------------------------------------- Yeap, the boys and gals at Jet Propulsion Laboratory (www.jpl.nasa.gov) use very powerful computer to calculate the neccessary trajectory changes required to send a spacecraft to a planet within our solar system. The most famous examples are the Pioneer and Voyager missions.
All this theoretical talk makes one wonder what a badminton game would be like off the Earth. Differences in gravity and atmosphere density would really change the game. Of course a game in open space would be neat, but I'd hate to have to retrieve the shuttle if I missed.
There is a very educational college physics video series, called The Mechanic Universe. It was aired in the eighties on the Knowledge Network in BC, Canada. It was filmed on location at the CALTECH and OXFORD.
And yes, vectors are very neat in computer simulation . Did you mention a minimum energy (elliptical) trajectory from Earth to Mars?
My first thought was how fast a Fu smash would come at me in a vacuum... Newtonian mechanics are only an approximation anyway, and have been superseded by relativity (but the equations are a helluva lot easier to deal with). The three body problem has yet to be solved, so we can't have two players and a shuttle in the same problem, let alone the planet on which they are playing.
whatever equation we have in Newton mechanics, badminton is a game where there are too many variables. the flight of the birdie will depend on, weight, angle of trajectory, air density, wind currents, drag coefficient of the feathers, angle of the feathers in the cone, width of the feathers, contact point of the shuttle with the racket, energy transfer between racket and shuttle etc. come to think of it, badminton is a supremely complex game with all these. Does it mean we are plain geniuses to make the game look simple?
Ahhhh, found it at last! http://www.learner.org/resources/series42.html http://www.learner.org/catalog/series42.html
then we have another P = mv so assuming we all swing the rackets at the same speed, then a heavier racket would have more momentum
actually, if you're being picky, it should actually be a=F/m which was also how Newton first came up with the formula. this is because on earth, acceleration is the dependent variable which changes with the amount of force which is applied. in situations where mass changes, e.g. accelerating to near light speed the it might be m=F/a. if acceleration is the dependent variable, then shouldn't it be on the left hand side?