Duration: flights to L-4 point, and 90 degrees Earth orbit

[Fred Bobo]

Assumptions:
200+ years from now
Asteroids have been moved to all Lagrange points, and at least 90, 180, and 270 degrees on Earth's' orbit for mining, and shielding humans and equipment
Tech to acceleration/decelerate at 1 gravity without need to carry fuel. (My main fiction.)
Direct line of flight

Space craft, tube shape, with decks perpendicular to line of flight.
Transport of crew, passengers, cargo: supplies, heavy tools,...

Mass: Similar to the Mont Oil Tanker(Knock Nevis, Jahre Viking, Happy Giant, Seawise Giant)
General Characteristics:
Tonnage: 260,941 GT (214,793 NT)
Length: 458.45 m (1,504 ft)
Beam: 68.8 m (226 ft)
Draught: 4.611 m (81 ft)
Capacity: 564,763 WT

Same mass, but dimensions reflecting the change in shape: Shorter length and larger diameter.

I am most interested in the duration of trips to the L4 point, and to 90 degrees forward Earth orbit,...Including the time to ramp up to 1g, the length of midpoint turnover, and the deceleration period.

Flights to all Lagrange points and to Mars L-points,... are of interest.

 

[mfb]

Including the time to ramp up to 1g, the length of midpoint turnover

This depends on your fictional method to accelerate.

L4 and L5 are 1 AU = 150 million km away, at a constant 1 g acceleration you can ignore orbital mechanics because you are much faster anyway. At a=1g you need $T=\sqrt{2d/a} = 120,000 s = 34 h$ to the midpoint and the same time afterwards, for a total of 68 hours or nearly three days (72 hours). Peak speed is 1200 km/s or 0.4% the speed of light.

 

[Fred Bobo]

Thank you.

would there not be a period of ramp up that will not exist at the end? Trying to visual.

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how about L1-3 and the moon for a craft 1/10-20th the size? Daily/hourly transports to the destinations within a 24 hour duration.

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I really wish i knew how to create a spread sheet with all the correct formulas.

 

[Fred Bobo]

Also: what do think the minimum acceleration should be to maintain human body health?

I think long hauls will be best to be at 1g. Shorter trips, even repeated often, will be less injurious. Or else not.

 

[mfb]

would there not be a period of ramp up that will not exist at the end? Trying to visual.

That depends on how your magic drive works. If it needs an hour or more to reach 1g then the trip gets a bit longer.

Chemical rockets can start within about a second.

how about L1-3 and the moon for a craft 1/10-20th the size?

Just plug in different values for d (half the length). a=10 m/s².We don't know the effect of reduced gravity on humans for a long time. We know 0 g for a long time is not so good, we know 1 g is good. For a few days it doesn't matter.

 

[Fred Bobo]

That depends on how your magic drive works. If it needs an hour or more to reach 1g then the trip gets a bit longer.

Chemical rockets can start within about a second.Just plug in different values for d (half the length). a=10 m/s².We don't know the effect of reduced gravity on humans for a long time. We know 0 g for a long time is not so good, we know 1 g is good. For a few days it doesn't matter.

Thank you. more to think about.

 

[hmmm27]

I'm not entirely sure you know what the terms you're using mean. Could you define (or better still, look up), please...

- 1 gravity acceleration : and what it means in terms of speed/velocity, and if there's a relation to mass/weight.
- ramp up
- turnaround : what it is and why it's used.
- LaGrange/LaGrangian/L points. (I'd suggest Wikipedia "LaGrangian points")

Basic kinematics formulae for distance, time, acceleration are also in Wikipedia (or here, it's a sticky post somewhere).

As DaveC points out, if you're going from Earth to L4 or L5, or other planets, at 1g, you don't have to worry much about orbital mechanics, because you're going (averaging) too fast for it to make much a difference, in an SF story where you'll presumably be saying "a few days" or "a couple of hours".

For messing about around the Earth<>Moon system, the grav sources are right in your face and the times are short (so massive velocities aren't built up), so yeah they'll make a difference there, as well as maybe throttling back a bit for passenger comfort in various circumstances.