>>I still don't understand why our current spacecraft travel so slow
>>in space. Can anyone explain?
I'm not sure "slow" is the word... Most would leave Earth in excess of 30,000 to 32,000 mph with respect to Earth.
>>For example a 500 day trip to Mars, with Mars at close
>>approach of 35 million miles works out to 2900mph.
That's true, but... no one is talking about a year and half mission to Mars. To *get* to Mars, it's estimated to be a 6 to 9 month mission - about 180 to 270 days.
>>That's no better than our top military jets that have to 'swim' through
>>our dense atmosphere, whereas space is a vacuum!
Agreed, but there are two things to consider: Fuel needed to boost the speed of the craft to reach Mars, and then - fuel needed to *slow down* for arrival at Mars... When Apollo went to the moon, they left Earth on a 'free-return' trajectory, meaning, if the engine failed, they'd loop back around towards Earth. It was a safety issue in case there were problems. (Apollo 13, for example, left Earth on Free-Return, then burned their engine to *leave* the free return trajectory... after the accident, their primary focus was to return to the trajectory to get back home...)
For Mars, there was a discussion about a proposed design that - if the engine failed at Mars Arrival, the speed of the craft would allow solar gravity to pull it back towards Earth - a 'fail safe' trajectory. But - the caveat is, you need to travel at a slightly slower speed than what's possible if you don't have 100% faith in your engine(s).
>>Also, we regularly go 17,200mph just to reach orbital velocity,
>>and need 25,000mph (?) to escape earth entirely.
Not precisely true; you need 25,000 mph to reach the moon, but it's not truly escape velocity...
>>So, how do we end up with a turtle 2,900mph once in space?
So... your 2,900 mph is based on an Earth/Mars straight line distance at closest approach. And, that's not the way to think about it. Below is an example of the trajectory a spacecraft would use... You'd launch about 6 months prior to closest approach, then intersect Mars' orbit on the other side of the Sun. It's a much longer journey than 35 million miles.
>>Is it a matter of fuel? If so, why can't we just shoot big tanks of liquid
>>hydrogen into earth orbit, send up our space craft, bolt the tanks on,
>>ignite the fuel and zip along at 25,000mph or even 100,000mph, at
>>least until the fuel runs out?
Partially - how much you can carry to boost your speed, versus how much you can carry to *cancel* your speed upon arrival. (And - the consideration of having a mass of volatile fuel on board for 6 to 9 months...)