Flying in my spaceship from London to Tokyo:

I know if I am just in orbit, I get from London to Tokyo, call it 20,000 km, 12,000 miles more or less, like half way round the planet, I can get there in about 45 minutes plus whatever time it takes to de-orbit and such. But how fast can I get there if I can vector thrust upwards to force my craft into a tighter curve, say I can thrust upwards or whatever the proper vector is to be able to make a faster curve around the Earth.
If I can take 3 g's (about the max on a space shuttle launch) how much faster can I get half way round the planet? If you envision a rocket, the flame would be pointing away from the center of Earth or maybe some vector off from there but one that allows the fastest curve flight half way round the Earth.

You can see if you just pointed the rocket motor in back like you would to achieve faster velocity with the goal of escaping Earth's gravity, or running in reverse to slow you down to de-orbit, but turning the rocket motor to shoot straight up would force you downwards but you would need some vector to speed you up AND force you downwards.

Originally posted by sonhouse
I know if I am just in orbit, I get from London to Tokyo, call it 20,000 km, 12,000 miles more or less, like half way round the planet, I can get there in about 45 minutes plus whatever time it takes to de-orbit and such. But how fast can I get there if I can vector thrust upwards to force my craft into a tighter curve, say I can thrust upwards or whatever ...[text shortened]... ld force you downwards but you would need some vector to speed you up AND force you downwards.

No takers?

Originally posted by sonhouse
I know if I am just in orbit, I get from London to Tokyo, call it 20,000 km, 12,000 miles more or less, like half way round the planet, I can get there in about 45 minutes plus whatever time it takes to de-orbit and such. But how fast can I get there if I can vector thrust upwards to force my craft into a tighter curve, say I can thrust upwards or whatever ...[text shortened]... ld force you downwards but you would need some vector to speed you up AND force you downwards.

Are you an ICBM?!

Originally posted by AThousandYoung
Are you an ICBM?!

More like a super super supersonic transport. It's a hypothetical space plane that takes off from a runway, accelerates like a bat out of hell in the atmosphere with ramjets and then uses high power rockets the rest of the way.

These rockets are nuclear powered so there is lots and lots of delta v available, it could just as easily fly to Mars than going to another spot on earth.

It's just that it has to be faster than just orbital velocity, there is a time deadline, they have to get this artificial heart to the president who just had a major heart attack in the middle of a jungle somewhere and they have to land the craft very close and get there in a half hour instead of the 45 plus minutes a space shuttle would take.

So they have the capability of several G's of accel but want to know the best way to use those rockets to force the orbit into a faster curve. The rockets can push straight up at the sky or straight down or back assswards so what angle do they push at and how many G's do they apply?

Originally posted by sonhouse
More like a super super supersonic transport. It's a hypothetical space plane that takes off from a runway, accelerates like a bat out of hell in the atmosphere with ramjets and then uses high power rockets the rest of the way.

These rockets are nuclear powered so there is lots and lots of delta v available, it could just as easily fly to Mars than goin ...[text shortened]... traight down or back assswards so what angle do they push at and how many G's do they apply?

your question is confusing. What orbital velocity are you talking about? Objects orbiting the planet are at a fixed location relative to a point on the earth? So if your in orbit above London, you stay above London.

Originally posted by joe shmo
your question is confusing. What orbital velocity are you talking about? Objects orbiting the planet are at a fixed location relative to a point on the earth? So if your in orbit above London, you stay above London.

I wrote an attempt of an explanation, but my internet momentarily fryed...leaving me with a blank screen and no motivation to redo my explanation. So I'll give you the short story and what I am at least 60% certain of

1. The problem is advanced enough that I'm only 60% confident in what im about to say

2. the problem is not easy and requires a tuned skills in calculus and classical mechanics

3. you do not have enough information to properly find a single solution

Originally posted by joe shmo
your question is confusing. What orbital velocity are you talking about? Objects orbiting the planet are at a fixed location relative to a point on the earth? So if your in orbit above London, you stay above London.

I am talking about LEO velocity, ~30,000 K per hour. Obviously if you were in geo sync orbit you would stay over the same place but low earth orbit you are going much faster. Since the gravity of the Earth is just so much, if you just fired the rockets aimed backwards to increase your linear velocity you would soon reach escape velocity and not return. I am talking about accelerating but with thrust aimed upwards to force the craft into a tighter curve than gravity would allow. Obviously a vector thing.