Solar Propelled Spacecraft
I heard on the news about Russians creating Solar
sails to drive their spacecraft in space. They say that the craft
could reach 100,000km/h in 100 days. (if they ever hear from it
again). This sounds like a great invention. How does it work? Do
photons have mass?
Photons do not have mass, but they do have momentum.
If the launch is successful, there is no reason why it shouldn't work in
principle. The mechanism is the transfer of the photon momentum from the
Sun to the "sails" of the craft. Photons do not have a rest mass in free
space; however, photons do have momentum. For certain types of spacecraft
the use of radiation pressure certainly makes both physical and economic
Photons do have mass. No "rest mass", but then photons are always moving.
The energy they carry has mass, and their velocity is the speed of light.
Easy formula: E=mc2, so m = E/c2.
momentum = mv = E/c.
If the sail is mirror-like instead of black, it can gain up to twice that
because the light isn't just stopped, it's reflected straight backwards.
Twice the velocity change, twice the momentum imparted.
It is a very dilute force, so your solar sail craft must be extremely
light and very broad.
In sunlight (at Earth's distance from our sun):
E/(area x time) = ~1kw/meter2 = 1000 J/m2.sec
thrust/area = momentum/time/area = E/c/time/area = E/(area x time)/c
= 1000 J/m2.sec / 3e8 m/sec = 3e-6 J/m3.sec2 = 3e-6 N / m2
For every square meter of sail area, it gets force equal to the weight of
0.3 cubic millimeters of water.
To accelerate at 1 earth-gravity,
imagine spreading a stack of 0.3mm high, 1mm square of water over an area
of 1 square meter.
Our 0.3mm stack would be 1 million times shorter; the sail would need to be
only 0.3 nanometers, 3 Angstroms, 3e-10 meters thick. About one atom thick.
We will not be making that real soon.
Fortunately, our spacecraft does not need a 1-g acceleration rate.
We can make the plastic sail 30-300 nm thick,
and do some useful missions with only 0.001 g,
given that it happens all the time, using no fuel.
Once a spacecraft is in stable orbit, it can adjust its orbit higher or lower,
more circular or more elliptical, or tilt the plane of the orbit, all
It needs to adjust the tilt of each of its sails rather often,
to control the degree and direction of its thrust,
its own orientation with respect to the sun,
and the rate of any pinwheel-like rotation it chooses to have.
It is potentially a bit of an ice-skating act,
a moderately challenging automated-control problem.
100,000 km/hr in 100 days implies an acceleration of 0.0003 earth g's.
Once one climbs out of earth-orbit, the sun-gravity at earth-distance is
about 0.001 g.
So this particular solar sail is not capable of escaping the sun on a
reasonably straight path.
It can only slowly change its Earth-orbit, escape into a sun-orbit after a
rather long time,
and then gradually change that orbit until it reaches some planet.
Later models might be capable of spiralling down near the sun,
then zinging almost straight outwards, starting a long drift towards some
But this one is the very first to try getting up there and maneuvering around.
I am enthusiastic too. Too bad it did not make it.
This spacecraft's homepage:
more technical details:
Java applet : fly your own solar sail Earth-to-Mercury mission:
(Much like the ancient computer game "Moonlander":
the hardest part is matching velocity, time, and position.)
Photons do not have mass, but they do have momentum.
If you're immediately uncomfortable with the idea that
something that does not have mass can still have
momentum, do not worry--lots of people are
uncomfortable with this idea.
Photons are packages of energy that travel as waves
which make up light. Einstein said that light always
moves with a speed (the speed of light, c). Because
the wave is always moving and never actually at rest,
it does not have a rest mass. We say that the mass of
a photon is zero.
However, waves do move through space with a frequency
and a direction, and do bounce off of things the way
that objects do.
This is how solar sails should work. Solar sails are
highly polished mirrored material. When photons hit
the sails, they will bounce off of them. When they do
this, the photon's momentum gets transferred to the
sail, pushing it in the opposite direction.
Let us take this back down to earth for a minute.
Pretend you are playing air hockey with two pucks. The
two pucks hit each other in the middle of the table
and bounce off each other going in opposite
directions. This is exactly how the solar sails and
photons interact. They collide, and bounce off each
other in opposite directions.
Another down to earth example is pool. You are hitting
one ball with the cue, which travels across the table,
and hits another ball. If you are a MUCH better player
than I, you can sometimes even get the ball you are
hitting to stop completely after it hits the ball you
want to move. This is because the initial ball has
transferred all of its momentum to the second ball.
In space, the sails are huge to let as many photons
hit them as possible. As each photon hits the sail,
it transfers its momentum to the sail, pushing it away
as the photon bounces off in the opposite direction.
Sadly, we did not get a demonstration of solar sails this time,
since Cosmos 1 crashed into the ocean. I will look
forward to the next time, when we will get to see them
Yes, photons have energy and, so, by Einstein's famous equation, E = mc^2,
they have a mass. Therefore, they also have momentum and so when reflected
undergo a change in their momentum which, by Newton's 2nd Law means a force
must have been exerted on them by the mirror. By Newton's 3rd Law, (action
= - reaction), the photons must then exert a force back on the mirror.
The force is very small for sunlight near the earth's orbit as you can tell
from experience. Even on the brightest day at the beach, you do not feel the
force of the sunlight on your body though you certainly feel the energy of
the photons as heat. Since p = E/c for photons (or any zero rest mass
objects), the large value of c (the speed of light) makes the momentum (p)
numerically much smaller than the energy (E) of the light.
For example, a sail with an area of 100 m^2 (about 30 ft by 30 ft) near the
earth's orbit will feel a force of about 1E-5 N (=0.00001 N) or 2E-6 lb.
Some steering is possible. For example if the sail is angled so the photons
are reflected to the left, the force on the sail will be to the right.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Update: June 2012