What is the fastest route to Earth 180

[Fred Bobo]

Scenario:
Large satellite arrays are at 90, 180, 270 degrees of Earth's orbit

What is the fastest route to Earth 180?

Possible fuels: liquid, solid, ion, sail, gravity

The best route?

Forward / backward ?

Thrust when, from?

Talk to me

 

[Bandersnatch]

You make a burn, using whatever propulsion system you have, in the prograde direction (i.e. forward in your orbit), which raises the apogee (the point of largest distance from Earth) on the other side of your orbit and makes the entire orbit take longer to complete. You do it until the period of your new orbit is one and a half as long as originally. You then turn off the engines, and let the orbit carry you along. After one orbit you'll return to the same point you started in, only now the satellite initially 180 degrees apart will be there too. At that point you need to turn around and apply thrust retrograde (backwards in your orbit), lowering the apogee, until your orbit is the same as initially.
You can do the same thing in reverse, by lowering your orbit (its perigee) and speeding up to arrive back to the starting point earlier (to meet the satellite), but you have to pay attention not to hit the Earth. With raising the orbit, you have to pay attention to stay in Earth's gravitational field (can't raise the orbit too much). What's more sensible depends on where the orbits are, exactly.
Also, these manoeuvres can be made less fuel consuming by raising/lowering the orbit just a little, and letting you catch the satellite after more than one orbit (less fuel consumption vs time trade off).

Illustrations and details here: https://en.wikipedia.org/wiki/Orbit_phasing

I suppose with fantasy-grade propulsion system that has good thrust and is not limited by how much fuel you can expand, you could just hit the pedal to the metal and go more or less in a straight line to your target, because orbital mechanics are for poor species.

(oh, poo, I thought you meant in orbit around Earth. Anyway, all the mechanics stay the same, just with different names)

 

[mfb]

Fly-by, or stay there?
How much mass should go there?

Accelerate forwards in the direction of Earth's orbit. You want an orbit with a period of 1.5 years, that way you are back where you started when Earth is at the opposite side. That needs a semi-major axis of 1.3 AU, or an aphelion of 1.6 AU. A bit outside of Mars' orbit, so you can use missions that went there as baseline. If you want to stay opposite to Earth you need another rocket stage after 1.5 years.
You can also accelerate backwards and aim for an orbital period of 0.75 years (and two orbits), that would need a semi-major axis of 0.82 AU and a closest point of 0.64 AU - closer than Venus, but again Venus missions give some idea how it works. Same arrival time, probably needs a bit more fuel but I didn't calculate that.
If you are in a hurry you can try to get an orbital period of just 0.5 years. That would need a semi-major axis of 0.63 AU and a closest point of 0.26 AU - significantly closer to the Sun than Mercury. Now you need a really big rocket and a really small payload, and staying at your destination becomes quite unrealistic if you want to have some relevant payload mass.

A Mars or Venus fly-by can save time/fuel, but it depends on the launch date.

 

[Fred Bobo]

Let us assume there is a large space array at 180. And docking is the goal.

Why go forward?

Meanwhile, back at the ranch: what can be the acceleration generation from a solar sail? Size related to payload. Over what period?

 

[mfb]

Why go forward?

Forward or backward are the fastest options with today’s technology. If you have stuff like nuclear pulse propulsion and need to get rid of a few thousand nuclear weapons you can ignore the Sun’s gravity and choose a more direct approach.

Meanwhile, back at the ranch: what can be the acceleration generation from a solar sail? Size related to payload. Over what period?

Small, and even smaller if you don’t want to accelerate away from the Sun. A pure aluminium foil from a kitchen provides an acceleration of 15 m/s per day under ideal conditions. Without payload or any material to keep it expanded, without steering and so on. By the time the solar sail gets going the chemical rocket is at its destination.

 

[Fred Bobo]

Thank you all for your responses.

 

[stefan r]

...

Meanwhile, back at the ranch: what can be the acceleration generation from a solar sail? Size related to payload. Over what period?

A solar sail's acceleration depends on the mass of your spacecraft (including sail and cargo), the surface area of the sail, and the distance from the sun. At Earth's orbit you can get 9.08 micro-Newtons per square meter if you have perfect reflection.
Solar sails make sense if you are trying to go cheap. You can use the Moon and Venus for gravity assists.