This document discusses proposals for interstellar travel using beam-powered propulsion techniques. It presents three main classifications of interstellar travel: 1) Relativistic reaction propulsion using nuclear or antimatter rockets, 2) Spacetime distortions requiring exotic matter, and 3) Generation ships. It then focuses on the basics and applications of radiation propulsion, including solar and beam-powered light sails. Models are presented for photon rocket kinematics, single trips to Alpha Centauri using antimatter rockets and beam-powered sails, and a two-stage laser-pushed sail concept for roundtrips requiring much less energy than other proposals.

1. Preparing interstellar travel
with ultrafast beam-powered lightsails
André Füzfa
University of Namur
Belgium

2. Interstellar travel and beam-
powered propulsion

3. The challenge of interstellar travel
★ Distance Sun-Proxima ≅ 10 000 x distance Sun-Neptune
★Voyager probes :
→ both launched in 1977
→ Voyager 2 now at 18 billion kilometers or 10-3 ly
→ Voyager 1 has record cruise velocity: 17 km/s
★Closest extrasolar system : Proxima Centauri at 4.4 ly (4.2x1013km)
★10 000 stronger propulsion, almost a billion more kinetic energy !
★ Or 10 000 times longer trips!

4. Classifications of interstellar travel proposals
1) Relativistic Reaction Propulsion
→ Nuclear energy (fission or fusion) rather than chemical to expel propellant
→ Antimatter rockets (direct or indirect)
→ Photon rockets or beam-powered propulsion (directed energy)
→ Energy cost : E~mc2 (~rest mass energy)
→ For 100 t ship: 16 x world annual energy production
NERVA fission nuclear
thermal rocket engine

5. Classifications of interstellar travel proposals
2) Spacetime distortions (wormholes, warp drives, etc.)
→ Require exotic matter with negative pressure (Dark Energy) at extreme density
→ Strong gravitational field => high compactness (=GM/(c2L))
→ Energy ~c4 L/G (with L the size of deformation)
→ For a one km-wide distortion : 1026 x world annual energy production
Interstellar
movie

6. Classifications of interstellar travel proposals
3) Generation ships
★Huge autonomous spaceships embarking a whole population at sub-light velocities
★ only the descendants (hopefully) arrive at destination
★ maintaining (intelligent) life in the ark during millenia-long trips
★ For a 10 000 yrs trip powered by 10 GW : 5 x world annual energy production
4) Faster-than-light travel
→ forbidden by conventional physics (special relativity)
→ useless for the relativistic traveler who undergoes time dilation
→ required only if you want to manage some galactic empire

7. Basics of radiation propulsion
★ Radiation pressure has many applications :
→ stellar equilibrium, cosmic microwave background, optical tweezers, plasma physics and H-bomb
;
→Yarkovski & YORP effects on asteroids ; comet tails Poynting-Robertson effect
→ Radiation recoil: gamma emission, Mossbauer effect, « black hole kick » from gravitational
waves
★Reaction force from momentum conservation of rocket + radiation beam
★ Thrust ~ Luminosity / c
→ 300 Megawatts of incoming light produce one Newton of thrust…
★ On-board powered propulsion :
→ Thermal photon rocket (blackbody radiation) ; matter-antimatter annihilation rocket
★Solar or beam-powered sail :
→IKAROS & NanoSail missions ; Breakthrough Starshot project

8. Beam-powered ultrafast probes
★ Pionneers of solar sails : Tsiolkowsky & Zander (<1930s)
★ Solar sail interesting for inner solar system not long distances
★Laser-propelled lightsails for interstellar exploration (Forward, 1962)
★ Forward ’s plan for interstellar rendezvous & roundtrips (1984):
→ space-based solar powered lasers
→ Phased array of lasers or huge (Fresnel) lens
→ Multi-stage laser-pushed sails
★ Most plausible proposal for interstellar travel
(after nuclear powered rockets?!)
★ Revival with Breathrough Initiative #3: Starshot (2016)
Starshot
project

9. A relativistic model for photon
rocket
See also : A. Füzfa,
« Interstellar travels aboard radiation-powered rockets »,
Physical Review D 99, 104081 (2019)

10. Relativistic kinematics for radiation rockets
★ Equations of motion :
→ Four-force : [fm]=(Power, 3-Force*c)
→ Four-momentum: [pm]= (E/c, 3-momentum)
→ t : proper time aboard the rocket
★ Total 4-momentum conservation : fm
total=fm
rocket+fm
beam=0
→ is conserved (r=rocket ; b=beam)
→ and, since , we have that
4-force on rocket
Beam 4-momentum

11. Relativistic kinematics for radiation rockets
★ For one-dimensional motion :
→ fT=±fX (rocket’s driving power = ± thrust*c)
→ Variation of rocket inertial mass (kinetic energy) :
→ Rocket’s driving power:
→ with y the rapidity (Velocity=c*tanh(y)) and m0 the rocket rest mass
→ valid for both radiation emission rockets and beam-powered sails
→ N.B.: for a free rocket m=m0 cosh(y) (see basic special relativity)
★ Specific solution: provide driving power P !
★Relativistic rocket equation (Ackeret, 1946):

12. Massive versus massless propellants
Ackeret Equation
(Relativistic propellant)
Tsiolkovski equation
(propellant at 10 000 km/s
exhaust velocity)
Tsiolkovski Equation
(massive propellant
At ~ 300 000 km/s
exhaust velocity)
Tsiolkovski’s
rocket equation :
Ackeret’s
relativistic rocket
equation :

13. Non-inertial effects aboard radiation rocket
★ Accelerated rocket at relativistic velocities : application of general relativity !
★ « Photon rocket spacetimes »
→ Vaidya’s shining star (1951) :
✦generalization of Schwarzschild spacetime to a particle at rest absorbing or emitting radiation
uniformly
→ Kinnersley (1969) :
✦spacetime around a particle accelerated by an anisotropic emission or absorption of radiation
→ Bonnor/Damour (1994) : « Photon Rocket spacetime »
→ Füzfa (2019) : application to the modeling of interstellar spaceflight aboard radiation
rockets
✦propagation of incoming/outgoing light, Doppler shift, aberration
✦Application to telecommunications and navigation

14. Stellar panoramas on-board
★ Deformation of the traveller’s local celestial sphere :
→ Aberration of light : shift of apparent positions of the stars
→ Doppler shift : change of the color of the stars
→ Relativistic focusing : increase of stellar apparent luminosities
★ Astronavigation requires correct astrometric measurements
★ Aberration of light : special and general relativity (acceleration to high
velocities)

15. 120° field of view around Alpha Centauri
in Earth sky (rest frame)
A taster
Southern Cross
Scorpion
& Sagittarius
Canopus & Sirius
Local sky seen by an accelerated traveller at 0.7 x c
Great Dipper
Little Dipper
Orion
Summer
Triangle

16. Applications
1- Manned mission toward Alpha Centauri aboard a matter-antimatter rocket
2 – Flyby at relativistic velocities in the solar system and beyond
3 - rendezvous with double-stage beam-powered sails

17. Single trip to Alpha Centauri (1/3)Velocityw.r.tEarth(c)
2) Cruise
1) acceleration
3) approach
Rocket proper time (years) Rocket proper time (years)Properacceleration(g)

18. Single trip to Alpha Centauri (2/3)
Initial mass :
100 t
Final mass :
~ 20 t
Maximum power:
a million of
GW power
plants!!
Energy cost = 74 x world annual energy production !!
Restmass(m0)
Rocket proper time (years) Rocket proper time (years)
Power(PW=1015W)

19. Single trip to Alpha Centauri (3/3)
Rocket’s time
Earth’s time
Total duration
in Earth’s time :
8.2 years
Total duration
in rocket’s time :
6.5 years
Time (years) Rocket proper time (years)
DistancefromEarth(ly)
Earthpropertime(years)

20. Duration is not the problem ; it is energy cost
Relations between travel duration toward Alpha Centauri (in time
aboard the rocket)
and cruise speed, energy cost ,
proper acceleration
N.B: initial mass = 100 t
Energy cost
(annual world
energy production)
Maximum local
gravity (g)
Cruisespeed(c)
On-board duration (years)
On-board duration (years)

21. Aberration of light
for the accelerated traveller
★Application of general relativity (Kinnersley spacetime)
★Deformation of the past light-cone
★Two contributions to apparent angle :
→ Variation of proper acceleration (« jerk »)
=> deviation of light geodesics
→ rocket’s velocity (special relativity)
★ Aberration of light is stronger than
expected with special relativity alone
A. Füzfa, Physical Review D 99, 104081 (2019)
In the cruise phase
During approach

22. Astronavigation with general relativity
Aberration of light from general relativityAberration of light due to special relativity
at 0.7 x c

23. Enjoy the panoramas during
your trip
Velocityw.r.tEarth(c)
Rocket proper time (years)

24. Applications
1- Manned mission toward Alpha Centauri aboard a matter-antimatter rocket
2 – Flyby at relativistic velocities in the solar system and beyond
3 - rendezvous with double-stage beam-powered sails

25. Model for laser-pushed sails
★Relativistic kinematics:
→ One-dimensional motion, pointlike photon rocket
→ Evolution of rapidity, mass, distance and duration in Earth time as a function of rocket’s proper time
→ Variation of driving power :
1. Decreasing with inverse square of distance from source (see also Kulkarni et al. 2018)
2. Doppler shift of the light flux
★Applications
→ Starshot project:
Power at source = 2 GW ; Initial mass = 1 g ; Beam divergence = 10-10 rad ; l= 1064 nm; Size of the sail = 10
m
→ High-velocity CubeSats :
Power at source = 1 MW ; Initial mass = 1 kg ; Beam divergence = 10-10 rad ; l= 1064 nm ;Size of the sail =
10 m

26. Accelerating phases
STARSHOT High-velocity CubeSat
Voyager 2 cruise
velocity record broken
after one month
of continuous shot

27. Kinetic energy gain and energy cost
2x1013J
of kinetic energy
for 1015J
energy cost
Free particle
in special relativity
(Kulkarni et al. 2018)
STARSHOT High-velocity CubeSat
1.5x1013J
of kinetic energy
for 3x1013J
energy cost

28. Distance charts
STARSHOT High-velocity CubeSat

29. Time dilation aboard
STARSHOT High-velocity CubeSat

30. Imaging during flyby at 0.2 c
Aberration of light in
General Relativity
Aberration of light in
Special Relativity
Reference

31. Applications
1- Manned mission toward Alpha Centauri aboard a matter-antimatter rocket
2 – Flyby at relativistic velocities in the solar system and beyond
3 - rendezvous with double-stage beam-powered sails

32. A two-stage laser-pushed light sail
★Roundtrip with multi-stage sails (Forward, 1984) :
→ accelerating phase with a large sail
→ Separation : outer ring goes on while the inner sail with payload is reversed
→ Approach thanks to deceleration with light flux reflected from runaway outer ring
★Same model as before but with double account for Doppler shift and flux decay with
distance + separation
→ Power at source = 6 MW ; Initial outer ring mass = 10 kg ; Initial inner sail mass : 1kg
★Energy cost~ 10-7 x world annual energy production for one probe

33. A rendezvous with Saturn in laser sails
Separation
Outer ring
Inner
sail
and
payload

34. A rendezvous with Proxima in laser sails
Separation
Outer ring
Inner
sail
and
payload
Power ~ 10 TeraWatts
Total mass = 100t
Payload mass = 10t
Total energy cost = 8 x world annual
energy production

35. Conclusions
★Main problem of interstellar flight is energy cost
★Directed energy for deep space propellant-less propulsion
★Modeling photon rockets with general relativity (trajectory,
telecommunications, astronavigation, etc.)
★Building a MegaWatt-scale solar-powered laser propulsion system
→ one expensive propulsing system but unlimited number of probes
→ break Voyager’s cruise velocity record
→ fast exploration of solar system with cube sats
→ test bench for beam-powered propulsion technologies and relativistic navigation
→ space debris and defense applications
★Paving the way to future manned missions into the solar system and nano-
probes interstellar exploration

36. A long path to the stars…
It is time to go beyond engineering sketches
and theoretical work…