# EM wave problem

physicsss
A beam of light carries momentum and therefore the absorption of a beam of light results in an impulse. One could contemplate constructing a solar sail that catches light the way a regular sail catches wind. One could even imagine trying to escape the solar system this way.

The sun has a mass of 2 × 10^30 kg and emits 4 × 10^26 W of power.
a) If the sail absorbs all of the light that reaches it, what is the maximum surface density the sail could have and still escape to infinity?
b) What if the sail is a perfect reflector?
c) How feasible do you think these quantities are?

can anyone explain to me what requirements are needed in order to escape to infinity so I can tackle part a? Thanks.

## Answers and Replies

Staff Emeritus
The answer depends on from where one is escaping - an orbit around the earth or from around the sun.

Then is it one time impulse or continuous.

For a one time impulse, one can set the kinetic energy equal to the required change in gravitational potential energy, in this case, to infinity.

Basically one has to calculate the kinetic energy equivalent to the change in gravitational potential energy between some point in the gravity field and infinity (where effectively the GPE = 0).

Please refer to - http://en.wikipedia.org/wiki/Escape_velocity#Calculating_an_escape_velocity

Otherwise, the power input has to equal the rate of change of gravitational potential energy.

http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html#ves

However, from the problem statement, it is not clear if one is to achieve the kinetic energy instantaneously or continously, which in the latter case would be decreasing as light intensity falls off as 1/r2.

Homework Helper
just set the Sum of Forces equal to zero.
Absorbing the Sunlight's momentum pushes the Area away from the Sun.
The Sun's gravity field pulls the mass toward the Sun.
(it is obvious - ignore the planets, ignore initial velocity)

b) Does reflecting transfer more momentum, or less, than absorbing?

c) how thick would aluminized mylar need to be (mass density about 1.6)?