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On November 3rd 1973, the Mariner 10 probe set sail for Venus where it gave us our first
close-up look of the planet, all the while lending it’s gravity to boost the probes
velocity to its next destination, Mercury. This mission gave humankind many of its first
experiences with space travel.
It was the first time a gravity assist had ever been performed using a planet’s gravity.
It was the first time 2 planets had been visited up close in a single mission, and it was the
first time solar pressure had been used to control a spacecraft’s attitude, but that
wasn’t by design.[1]
This mission came incredibly close to being a complete failure as a result of debris floating
around the spacecraft interfering with the star tracking navigation camera. Each time
it happened Mariner 10 needed to perform a corrective roll to reacquire a lock on Canopus,
it’s reference star. [2] To make matters worse, this occurred more frequently as the
brightness of the particles increased as Mariner 10 approached the sun.
Mariner 10 managed to complete its gravitational slingshot by Venus and was now limping on
to Mercury but was quickly running out of nitrogen, the propellant needed to perform
these maneuvers. To solve this problem, the engineers came up with a genius plan. By tilting
the solar panels they could use solar pressure, the force exerted by photons, to control its
roll and stabilize its position.
A huge moment that proved the viability of solar sails for future use in spacecraft,
and just this year Lightsail 2 provided a valuable technology demonstration of solar
sails ability to provide control at a very low cost for small satellites. [3]
Before we jump into what Lightsail 2 achieved, let’s first see how it works.
Although photons don't have mass, they do have momentum, which can be transferred into
an object with a reflective surface[3]. This is a bit counter intuitive for anyone that
has learned, like me, that momentum equals mass by velocity, so we need a new equation
to describe the momentum of a photon, and here it is. The momentum of a single photon
can be found by dividing Planck’s constant by the wavelength of the photon. Since Planck’s
constant, is well….a constant. The momentum of a photon is entirely determined by the
wavelength, with shorter waves having higher momentum. [4] Finding the momentum for a wavelength
of 500 nanometres, we can find a momentum of just 1.33 x 10 to the minus 27 kilogram
metres per second. That’s obviously tiny, but when dealing with the vacuum of space
that can add up when every single collision of a photon with the solar sails provides
an increase in velocity of the spacecraft, thanks our friendly neighbourhood laws of
physics, or the conservation of momentum to be exact,
which states that the change in momentum of a photon must involve an equal and opposite
change in momentum for the object it interacted with.
We can maximise this transfer of momentum by ensuring the sail is as close to a perfect
mirror as possible, wasting as little energy as possible to the heating of the sails.
But this isn’t the only factor that varies the force a lightsource can impart on a solar
sail.
A less friendly neighbourhood law of physics, the inverse square law, states the intensity
of a point source of energy, say the sun, will decrease with the square of the distance
away from it. This is a result of the energy spreading over a greater area as it radiates
outwards. This basically just means less photons will hit the sail the further away it is from
the sun. So if a solar sail was double the distance from the Sun, it would only receive
a quarter of the photons. Triple the distance the sail would receive one ninth.
This makes the solar sail increasingly ineffective as we travel to the outer edges of the solar
system and beyond.
The other primary factor that affects the force imparted onto the sail is the angle
at which the photons strike the sail. You can think of this like a game of pool, where
the angle the queue ball strikes another ball will determine the direction it travels in.
Or you can dispense with the useless analogies and think of it as a photon bouncing off a
mirror. The direction of thrust will always be perpendicular to the mirror and vary with
the cosine of the angle of incidence. When the sail is perpendicular to the incoming
photons the incidence angle will be zero and the cosine of 0 is 1, and thus it will be
at a maximum. Of course the effective area of the sail also decreases as it angles away
from the sun. The effective area can be found by multiplying the total area by the cosine
of the incidence angle, and thus the force really varies with cos squared of the incidence
angle. [5]
Putting all this theory to work we can see how the Lightsail 2 achieved its goals.
Lightsail 2 was a project by the Planetary Society, a company formed by Carl Sagan, Bruce
Murray and Louis Friedman back in 1980, with a goal of raising funds for exciting missions
through crowdfunding.
It is currently run by my buddy Bill Nye, as you can see here he totally knew who I
was and didn’t think I was just a fan nervously asking him for a photo.
Lightsail 2 is a tiny craft weighing just 5 kilograms and 11.3 centimetres in width
and 34 centimetres long, but when deployed the sails had an area 32 metres squared.
This compact size allowed it to ride share on a Falcon Heavy mission in June 2019, launching
into orbit around earth at 720 kilometres. [3]
When Lightsail 2 is moving away from the sun, it faces its sail towards the sun to maximize
the acceleration. Then, as it moves back towards the sun turns on it’s side so the solar
sail isn’t slowed down, but as the earth blocks the sun for about half of its orbit
we are only really getting thrust for about one quarter of its orbital period.
This regular adjustment of orientation will make a solar sail in planetary orbit heavily
dependent on reliable control moment gyros, and as the sail grows in area the more demanding
this requirement will be both on the size of the equipment needed, and the energy required,
but the technology does exist.
By performing this maneuver every period, LightSail 2 managed to raise its apogee by
2km in its first week of solar sailing[6]. However, the lowest point of its orbit or
its perigee has been decreasing at a faster rate. [7] Meaning the orbit energy of Lightsail
2 is actually decreasing.
This is happening primarily because the spacecraft still comes into contact with Earth’s atmosphere,
even at 720 kilometres. Since the solar sail by design has a large surface area with very
little mass, the small traces of atmosphere found at 720km are enough to significantly
slow down the spacecraft’s velocity. This drop in velocity causes the spacecraft to
dip further into the atmosphere where the drag increases, slowing the spacecraft down
even more. Because of this, Lightsail 2 is expected to deorbit in about a year. This
could have been mostly avoided if the spacecraft was placed into a higher orbit where it would
experience more solar pressure and less atmospheric drag. The point at which these two pressure
equals is around 800-1000 kilometres above earth’s surface [8], so any useful solar
sail would need to be launched higher than this.
Nevertheless, the increasing apogee of Lightsail 2 has proven that solar sailing could be a
useful technology for future space missions, but I’m not sure why we needed to prove
that since Mariner 1 did that 40 years ago….it in the least provided additional data and
design verification for future solar sails.
So beyond this not so ideal application, how could we potentially use lightsails to develop
new technologies.
One of the most important perhaps could be an early warning system for solar flares.
To do this we would need a spacecraft to keep a position directly between the earth and
the sun. Anyone familiar with Kepler’s laws of orbital mechanics will know this difficult,
as any object orbiting closer to the sun will have a higher velocity and shorter orbital
period. So it would be racing ahead of earth. To maintain this position a spacecraft would
need to constantly push back into position, and obviously propellant would pretty quickly
run out. So solar sails are the perfect solution for this, and they will be able to achieve
more thrust the closer they get to the Sun.
We already have several satellites for this purpose parked in lagrange point 1, which
is the point at which the gravity exerted by Earth and the gravity exerted by the Sun
is the same. However a solar sail with a 67 by 67 metre area would allow a satellite to
double its distance from Earth, and thus provide double the warning time at about 2 hours.
This would provide Earth vital time to prepare for a solar storm and protect our satellite
in orbit and our grid system. Larger sails would allow the satellite to park even closer
to the sun, but we begin to run into engineering challenges as we approach the Sun with unpacking
the larger sail and protecting it from the Sun’s heat [9]
If we had suitable materials that could be both extremely thin, reflective, light and
heat resistant, we could sail even closer to the sun to perform sun diving maneuvers
to capture the Sun’s energy to increase our velocity and explore the outer solar system.
There are countless other applications for this technology that you can learn about with
the referenced material in the description, but you may have difficulty understanding
them without a decent understanding of orbital mechanics. I started to read up on this subject
myself in anticipation for the new Kepler Space Program game, and Brilliant’s course
on Gravitation Physics will teach you everything you need to know about Keplar’s laws of
orbital mechanics and much more.
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