# Laser Launching

Lasers seem to be on my mind recently. Just yesterday, the class I TA
for (E&M for engineers) talked about the momentum carried by E&M waves.
This called to mind a discussion I had with a housemate a few weeks
back. He had heard somewhere that ‘they’ were thinking of launching
satellites with lasers. *No way*, I thought to myself. *Satellites are
too heavy*. However, his question has been hovering around in my mind,
so I’ve decided to try and answer it: can we use a laser to launch a
satellite into orbit? Let us begin with a few simplifying assumptions.
I’m going to assume that we want our launched satellite to reach the
escape velocity of the earth. Of course, we don’t want a satellite to
escape orbit, but escape velocity is calculated without considering any
kind of drag forces on our launched object. To first order then, I
expect achieving escape velocity will get our satellite into a
relatively high orbit without actually escaping earth’s gravity well.
Second, I’m going to assume our laser is on the ground (reusable
launching device!), and that our satellite is perfectly reflective, so
we’re not going to be melting it. Finally, I’m going to assume that the
laser will remain effective at targeting our object up to 15 km above
the surface, around the effective range for lasers used as guides for
adaptive optics in
telescopes.
Now, to the meat of the problem. First, we need to find the escape
velocity from the earth. This is defined as the velocity we would need
to give an object to overcome the gravitational energy of the earth upon
the object. This is found by setting the kinetic energy of the object
equal to the change in gravitational potential energy from the earth’s
surface to infinity:
*10^14W. This is .5 PW.
According to wikipedia, the greatest power output of a continuous
operation laser is on the order of 1 kW, or \~10^12 times less than our
necessary power! There’s no way we’re getting a normal sized satellite
into orbit with a laser. What about a smaller satellite? In recent years
picosatellites have proposed, with masses of \~.1kg. This gives a
necessary power of 6.2*10^10, or 620 TW. This is still \~10^8 times
greater than our most powerful continuous laser. In fact, reversing the
calculation, our laser could launch a satellite with a mass of \~1.6 mg.
A little googling reveals this is the same order of magnitude as a grain
of rice! Simply put, we’re not going to be launching satellites with
lasers anytime soon.

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