Concordia

Getting there from L5

Concordia floats in the Earth-Moon L5 region, 384,400 km from Earth. A passenger leaves on a 10 km electromagnetic launcher, which gives the first push for free, and then flies a 15 day path past the Moon to Earth. The launcher is only the first leg.

What the tags mean

Why L5

A Lagrange point is a spot where the pull of two bodies and the motion of the orbit balance. L5 trails the Moon by 60 degrees on its orbit, at the same 384,400 km from Earth, forming an equilateral triangle with Earth and Moon. In the idealised picture, with Earth and Moon on circular orbits and nothing else pulling, L4 and L5 are stable: a small push sends an object into a slow loop around the point instead of carrying it away. The other three points are not. L4 and L5 stay stable only because Earth is more than 25 times heavier than the Moon; it is 81 times heavier. Established physics

The real world is messier. The Sun pulls, the Moon's orbit is not circular, and ship traffic and cargo launches all push on a station of this size. So Concordia is station-kept: continuous navigation, and low-level correction by high-efficiency electric thrusters. Twelve thruster pods ring the aft face, with a combined power around 108 MW and a specific impulse near 3,000 s. Large manoeuvres take days or weeks. Engineering challenge

L5 was chosen for five reasons: low-energy access to lunar material, access to Earth and the cislunar network, no planet below, a huge volume for construction, and a staging point for travel onward. The station moves around Earth at 1.018 km/s. Established physics

Earth and the Moon hang in black space beside the long grey habitat, showing the station far from either world at L5.
Concordia at L5 with the Moon far off in the black. The Moon is the quarry and Earth is the market, and this point gives low-energy access to both. Open this view

The launcher: first leg only

The passenger launcher is a track about 10 km long on the outside of the hull. A carrier on a levitated keel accelerates at 1.5 g for 37 seconds and leaves the end at about 540 m/s. Nothing touches the track at speed. Engineering challenge

It costs 28.5 GJ per launch, 0.77 GW on average and 1.56 GW at the peak, a few percent of the station's power. In return the shuttle saves about 30 tonnes of propellant. It does not reach Earth by itself. 540 m/s is a fraction of what the trip needs, and everything after it comes from the shuttle's own engines and the Moon. The station does not turn quickly, so launches go in scheduled windows. Design value

The electromagnetic launch track and its gantries running along the outside of the station hull.
The track from outside: gantries and a levitated keel run 10 km along the hull. Nothing touches the track at speed. Open this view
Inside the passenger launch cabin: rows of couches, a window band, aisle lighting and the shelter bulkhead.
The ride from inside: 98 couches, a window band and a shelter bulkhead, held at 1.5 g for 37 seconds. Open this view

Set a track length and an acceleration to see launch time and exit speed. At 10 km and 1.5 g the answer is 37 seconds and about 540 m/s.

Open in the simulation: Ride the launch Open in the simulation: Launcher Track: External Open in the simulation: See the whole habitat

The delta-v budget

Delta-v is the change in speed a ship can make, the standard currency of spaceflight. After the launcher, the shuttle spends about 665 m/s on a one-way trip to Earth capture.

The 15 day Earth transfer, schematic Not to scale. Earth at left, the Moon on its orbit to the right, and Concordia at L5, 60 degrees behind the Moon on the same orbit. The path leaves L5 at day 0, swings past the Moon at day 6, and reaches Earth capture at day 15, where a 395 metre per second burn at 400 kilometre perigee enters a long orbit of about 21 hours. Earth Moon L5 (Concordia), day 0 Swing-by, day 6 Capture, day 15 Moon's orbit, 384,400 km Propulsion after the launcher Departure burn: 250 m/s Lunar swing-by: 0 m/s Midcourse: 20 m/s Earth capture: 395 m/s Capture orbit: 400 km by 70,000 km, about 21 h per lap. Schematic: not to scale.
The path from L5, past the Moon on day 6, to Earth capture on day 15. Not to scale.
Step Delta-v Where
Launcher 540 m/s The track, no propellant
Departure burn about 250 m/s Leaving L5
Lunar swing-by 0 The Moon bends the path
Midcourse about 20 m/s Trim
Earth capture 395 m/s At 400 km perigee

The return leg is estimated at 780 m/s. With methane and oxygen engines at 380 s specific impulse, the shuttle burns 68 tonnes of propellant for a round trip, 53 t of oxygen and 15 t of methane. The oxygen is the part that comes from the Moon. Only the carbon and hydrogen for the methane have to come from elsewhere (see materials). Established physics

Fifteen days and a Moon

The path takes 15 days. A transfer orbit is a path from one orbit to another. This one is slow on purpose: the shuttle spends time instead of propellant. At day 6, 42 percent of the way, the shuttle swings past the Moon with its engines off. A gravity assist lets the Moon's gravity bend the path, at no cost in propellant. From the window the Moon is huge: at the closest approach it is about 50 degrees across, a hundred times wider than it looks from Earth. Earth starts at 1.9 degrees and grows to about 10 degrees later in the trip. Established physics

Then comes the capture. At a perigee of 400 km the shuttle fires its engines for 395 m/s and enters a long orbit that reaches out to 70,000 km from Earth's centre, one lap in about 21 hours. This burn is what turns a fly-by into an arrival.

The Moon filling much of the view at true scale as the shuttle passes it on the way home, with Earth small and far beyond.
The Moon at true scale during the swing-by. Open this view

Open in the simulation: Fly past the Moon Open in the simulation: Home, seen from afar. Open in the simulation: Earth / Moon / Habitat Context

Entry and the shuttle

The Earth shuttle is a 64 m stack of two parts. The carrier holds propellant and four 160 kN methalox engines and never enters an atmosphere. The coach holds 98 couches, 96 passengers and 2 attendants, is built as a lifting body, and lands on a runway. The stack weighs 196 tonnes at launch and carries an 18 tonne water storm shelter. Design value

At the end of the transfer the coach separates and meets the air at 11 km/s. That is almost Earth's escape speed, the speed anything falling in from far away reaches, and it is the hardest part of the trip for the heat shield.

Earth filling the window as the shuttle falls toward its perigee, with the curve of the atmosphere lit along the limb.
Earth filling the window as the stack falls toward perigee. Open this view

Open in the simulation: Arrive at Earth

Go deeper: Worked example: launch and entry Established physics

Launcher: a = 1.5 × 9.807 = 14.7 m/s². Over L = 10 km, v = √(2aL) = √(2 × 14.7 × 10,000) = 542 m/s, in t = v ÷ a = 36.9 s. The energy for a 196 t stack is ½mv² = 0.5 × 196,000 × 542² = 28.8 GJ, in line with 28.5 GJ over 37 s, an average of 0.77 GW.

Propellant: the exhaust speed of a 380 s engine is 380 × 9.807 = 3.73 km/s. By the rocket equation, Δv = vₑ ln(m₀ ÷ m₁), so 665 m/s needs m₀ ÷ m₁ = e^(0.665 ÷ 3.73) = 1.195, which is about 16 percent of the starting mass in propellant, one way, before the return.

Entry: a body falling from the Moon's distance to a perigee 120 km above the surface (r = 6,498 km) reaches, by the vis-viva equation,

v = √( μ × (2 ÷ r - 1 ÷ a) )

with μ = 398,600 km³/s² and a = (6,498 + 384,400) ÷ 2 = 195,449 km, v = 10.98 km/s. Earth's escape speed at that altitude is √(2μ ÷ r) = 11.08 km/s.

Sources and further reading

Real-world sources

  • "Lagrange Points of the Earth-Moon System", HyperPhysics, Georgia State University: hyperphysics.gsu.edu.

Concordia design documents

  • Concordia engineering specification, sections 2, 31, 32 and 42, and the Earth shuttle and aft-end design notes.
  • Materials from the Moon and asteroids Concordia is made almost entirely of the Moon and of asteroids. The Moon supplies oxygen, metals, glass and bulk stone.
  • Moving around a spinning world In Concordia you walk, ride the metro, take a lift to the axis and cross to other rotors by train. Each trip feels a different piece of the spin.
  • The spaceport Everyone who arrives from Earth or the Moon comes through the spaceport at the forward end.
  • A day aboard A family of five lives in the Arbor Quarter of Tsiolkovsky (Rotor 1). Today they leave Concordia for Earth.