Virtual Galactic again!

I know that to overcome these problems the old sci-fi solution of rotating would probably work. Not a physics master, so I might be wrong.

Possible, but a very awkward solution - there is a much 'sleeker' one!

First off, I thought Ben's idea was effective.

I know in a circular orbit you are continuosly falling at the same rate that the curvature of the Earth is falling away resulting in a feeling of weightlessness. I wonder if an elliptical orbit would do the trick.

Yep, Ben's idea may be effective, but cumbersome. How do you rotate a spaceship fast enough without having 'sick' passengers?
Normal elliptical orbits won't do either – it's weightlessness all the way, because it's still a free-fall.

What about that "long-playing 1g-acceleration propulsion system" stated in the puzzle?

At an altitude of 200 km you are 6578 km above the center of the Earth. If you circle the Earth at an circular velocity of 8 km/s you will produce a centripetal acceleration of about 9.7 m/s^2. That acceleration will be close to that of Earth at the surface.

8 km/s is much, much faster than the normal orbital velocity for that altitude, so you will be constantly burning fuel to turn the spacecraft toward the Earth's center as you go around the Earth.

A better way is to rotate the space ship about a distant center. You can do this by placing an equal mass to the spacecraft at a long distance away and set both the mass and the spacecraft into spin where one flips over the other. The problem with this arrangement is that there are problems with the inner ear's balance due to the spin. Sudden movements can cause disorientation. To deal with this the radius of the spin must be very large so that the rate of spin is low. Theoretically, if the rotation rate is slow enough and the radius long enough, the disorientation is reduced to the point where it is negligible.

Both methods are really difficult to employ, but the degree of difficulty in generation artificial gravity by spinning the craft about a long radius is probably several orders of magnitude easier than track racing around the globe at 8 km/s!

I might clarify the above statement. Think of the spaceship as your car. If you drive fast in a tight circle you experience a lateral acceleration. The spacecraft is doing the same thing, but the radius of the circle is very large and the velocity must be even larger. You must keep the steering wheel turned into the turn's radius. In a spaceship you need to do this using thrust. So you have two vectors; one is tangent to your orbit and one is toward the radius of the orbit. It will take a lot of thrust to do this and you had better hope you don't make contact with even tiny debris at those velocities.

The formula is a = v^2/r, so the square of the velocity divided by the radius of the orbit yields the centripetal acceleration.

Two nice tries, but:
Your 1st solution: ("At an altitude of 200 km you are 6578 km above the center of the Earth....") I get 9.2 m/s^2 gravity at 6578 km radius. Normal orbital velocity there is 7.9 km/s and that gives weightlessness; in other words, the gravitational centripetal force is balanced by the centrifugal force. At 8 km/s horizontal velocity at that altitude, while constantly thrusting at 1g towards Earth's center, will quickly drive you into the atmosphere and be destroyed!
Your 2nd solution: ("A better way is to rotate the space ship about a distant center...") That may work in empty space, far from any gravitating mass, but that's not what Virtual Galactic sold tickets for. They promised to orbit at 200 km altitude at our familiar 1g 'weight', for a comfortable and (presumably) perfect view of mother Earth with no space sickness!
What about combining your two solutions?

Oops! There's a typo in my: "Normal orbital velocity there is 7.9 km/s.....". Should read 7.8 km/s (more accurately 7.78).

Yes, you are right. Shame on me. You need to slightly more than double the speed of the normal orbital velocity.

However, you don't aim the rocket at Earth and thrust at 1 g. No, no, no! The concept is to "drive" the rocket in a circle with a radius of 6578 km about the center of the Earth.

I forgot to add the velocity of a normal orbit at that altitude to my calculations. Just don't let me drive!

I don't think your concept of "driving the rocket" like a race car turning into the track will work. It may not even be a very good analogy.

In a stable orbit, as noted by others, passengers experience weightlessness, as the ship is in "freefall" around the earth. Velocity is constant. Any increase in velocity would result in a higher orbit and any decrease in a lower orbit. If you look at it vectorially, a 1g burn at some angle other than directly towards the planet's surface will result in a positive acceleration vector in the same direction as the orbital velocity vector, causing an increase in the orbital velocity, and therefore a resulting higher altitude above the earth.

I am not sure of the math at this point, but essentially you have an increasing orbital radius, so whether it is elliptical, parabolic, or some other curve, eventually you must turn the ship around and resume your 1g burn in the opposite direction, presumably about halfway through the trip, slowing the ship for a landing and reducing its altitude. Otherwise, get ready for interplanetary flight!

Alternative ship design, with retro rockets in the nose and reversible passenger seating or compartments would eliminate the need to turn the whole ship around. In fact swivellable seating/compartments would be ideal because at some point as the rocket slows down and reduces speed and altitude, i.e. leaving orbit, gravitational effects begin to be felt by the passengers, so a variable angle can keep the acceleration vector normal to the "floor" of each compartment, maintaining at least the illusion of normal gravity. Due to required flight trajectories, the actual acceleration might vary from 1g.

Seriously, though, I cannot imagine that the first orbital passenger flights will have anything of the sort. First of all, it would be terribly wasteful way to use energy. Secondly, I would think part of the appeal of an "orbital trip" around the earth would be to experience weightlessness. Incidents of "space sickness" should be no greater than "air sickness" experienced by airlines today.

Orbital velocity decreases with higher orbits.

I think flying an orbit at high speed is the right answer. You can do the same thing in an aircraft, but the wings are what turns the aircraft in a circle. For a spacecraft it would be vectoring the thrust so the craft flys in a circle which is a circle with a radius of 6578 km.

It is a very wasteful effort concerning fuel use!

Your last statement is absolutely correct. People would want to experience weightlessness. I know I would and do it when I fly sometimes just to enjoy 0 g and high g manuevers.

OK, so now we 'drive' the spaceship around Earth at 200 km altitude at your proposed speed of 7.8 + 8 = 15.8 km/s. For a circular orbit, I calculate a required centripetal acceleration of 37.95 m/s^2. Subtract 9.2 m/s^2 for gravity at 200 km and we are left with 28.75 m/s^2, or almost 30g!

Virtual Galactic's propulsion system can't cope, which is just as well for the sake of the passengers! Weren't they promised 1g?
I think I have given away the solution above! As an aside, can Virtual keep the acceleration at 1g right from lift-off and throughout the flight until landing?

Yes, next time I will stop and do the math first! The square of the velocity is the key in the equation and I should have just worked the math before sending.

A 1G lift off and return? That is even more fuel for such a slow ascent and it would have to be horizontal for a long portion of the lift off since even an elevator or ballon going upward increases g force beyond one g. Any acceleration is going to add additional force to the passengers in some vector. As for descent, you would need to hit the atmosphere at a crazy velocity, but once you can get into the atmosphere a set of wings could allow you to do some creative flight patterns to maintain g.

If you boosted through the center of the earth starting at 2gs and then slowly reduced thrust to 1g near the center and 0g at the opposite surface (continuing thrust is only enough to maintain velocity) then you would emerge traveling very fast, your passengers would only experience 1g, and as a bonus they would experience less time then all thier friends on earth. I recognize that this is an impractical solution.

If you were traveling at about 11000 m/s, which is what you would need for a centripedal acceleration of 9.81 m/s^2, you would need a thrust of 1g towards the center of the planet in order to maintain orbit. I was thinking of dangling a mass, maybe an observation deck, down the well where the velocity of the mass would be much less then orbital velocity. This way the weight would provide the additional force (towards center) needed to keep the shuttle from heading for the stars. However it appears that the weight would have to be under the earths surface, or the acceleration of the craft would have to be lower (wouldn't the whiney passengers be happy with 1/4 g). I'm fresh out of silly ideas.

I haven't worked the math, but an interesting side note to all of this is the idea of a stationary "rope" elevator to low Earth orbit. With advancement of nano tubes made of carbon, there are a few companies researching this idea.

Rather than using a heavy lift rocket to get payload into orbit, a stationary rope ladder which a machine can ascend to the top would be cheaper and a lot less complicated.

What I don't know is what you would anchor the far end to! It would need to be geostationary and a geostationary orbit is a long way out there. Also, how do you keep the thing aloft? The weight of the system would be a variable drag (depending on use and the payload) on the anchor in orbit.

One of my first thoughts was if it was possible to tether a mass at the end of one of these rope elevators at an altitude that would keep the system up in orbit. Daunting question!

So, anyone know the answers?

It is possible (in principle) to hang a cable from any orbiting satellite. It has been done in the past to keep the same side of the craft pointing to Earth without having to use thrusters for rotational control. How long one can make such a cable is probable not known. It will surely have to be above the atmosphere. As far as I know, NASA did once try to generate power by hanging a long conductor down, but the cable snapped on deployment.

A typical orbit results in weightlessness because centripetal (gravity) and centrifugal forces are equal and no acceleration is present. If acceleration is introduced (1g ?) we still have an orbit albeit a different altitude. At 1g we have the added benefit of being able to stand still at any altitude. Of course I am at home and can't try this.

Launch your spaceship straight up to 200 km. Use your 1 g continuous thruster to hold your altitude and slow the craft down so that the Earth rotates under it. About 2% of your 1 g thrust would be used to change the craft's orbital speed, the rest holding the craft at a fixed altitude as gravity is a little less at 200 km above the Earth's surface. After the Earth has rotated half way under the craft, alter its attitude so that it is now accelerating to catch up with the Earths relative rotational speed, while maintaining the fixed 200 km altitude. It's going to take around 8 hours to accomplish one orbit around the center of the Earth, less if the route holds at say a fixed lattitude. Because you are not in free-fall, it is not necessary to have an orbit about the center of the Earth.

A very interesting solution! I think you will have 6% of the 1g thrust available for changing the craft's orbital speed, because gravitational acceleration at 200 km is about 9.2 m/s^2. If you keep going in one tangential direction (slowly orbiting Earth), your speed will increase until you reach normal orbital velocity. After that you will have to thrust more and more inwards to prevent the orbit from increasing in radius, until you reach about escape velocity (11 km/s), from which point the thrust must be to the center of Earth. Or am I missing something?

I did not do the math, just trying to think logically. By continually adjusting the thrust attitude, altitude could be maintain constant unless the thrust was nearly directly down or directly upward. So the thrust would have to be quickly rotated through those positioins or rotated around those positions (think 3 dimensions), otherwise that is what I am saying.

Because it is powered flight, there is no reason why tangential speed could not be accelerated or decelerated at will, so it would not be necessary to reach the orbital speed where downward thrust is needed.

Agree with "Because it is powered flight, there is no reason why tangential speed could not be accelerated or decelerated at will....". In my scenario, that is what I will do to slow down for 're-entry' and landing again. The idea of such powered flight will have to wait until "free energy" becomes online - which is probably in the "infinite future", whatever that may mean. So this is sci-fi!

Wait! Since this "Virtual Galactic" there is no need for all of this! All you need to do is provide a video feed from a small spacecraft in orbit to your customers.

After all, this is a virtual space tour. Your client never needs to leave the comfort of their own living room.

Virtual Galactic - Where no one has gone before and is likely not to go in the foreseeable future.

Ah!!! The final and only precise answer! But it was nice 'waffling' about other possibilities. Thanks to everyone who participated.