Physics - Photons and Solar Sails

Forces and Momentum Written Questions

What is the momentum change when a photon is absorbed by a solar sail?

Δp=p (photon stops, transfers its momentum).

What is the momentum change when a photon is reflected off a solar sail?

Δp = 2p (photon reverses direction, doubling momentum transfer).

How do photons exert force on a solar sail?

By transferring momentum when they reflect or are absorbed.

Why does reflection exert more force than absorption?

Because reflected photons reverse direction, causing a 2p change in momentum, compared to only p for absorbed photons.

What physics laws explains why a solar sail moves forward when light hits it?

Newton’s Third Law – the photons push back on the sail as they reflect.

What formula relates force and momentum change?

F = Δp​/Δt

What formula relates force and acceleration?

F = ma

How does increasing photon reflection affect acceleration?

More reflected photons → Greater force → Greater acceleration.

What are photons?

Photons are the smallest possible particles of electromagnetic energy and therefore also the smallest possible particles of light.

A given solar sail has a highly reflective surface. Explain why photons of light reflected from the solar sail can result in the acceleration of the solar sail.

Why a Reflective Solar Sail Accelerates When Hit by Photons

1. Photons Carry Momentum

Even though photons have no mass, they still carry momentum given by:

p = E/c

where E is the energy of the photon and c is the speed of light.

When photons strike the solar sail, they transfer momentum to it.

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2. Reflection Causes a Greater Change in Momentum

• If a photon reflects off the sail, its momentum reverses direction.

• The total momentum change per photon is: Δp = pf −pi = (+p) −(−p) = 2p.

• This means the force exerted on the sail is twice as large as it would be if the photons were absorbed (where Δp = p).

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3. Newton’s Third Law – Reaction Force on the Sail

By Newton’s Third Law, when the photons exert a force on the sail by changing their momentum, the sail experiences an equal and opposite force, pushing it in the direction of the reflected photons.

Since this process occurs continuously with many photons, the sail undergoes constant acceleration in space.

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Conclusion

A highly reflective solar sail accelerates because photons reflecting off it experience a greater change in momentum (2p instead of p), which doubles the force acting on the sail. By Newton’s Third Law, this results in a greater acceleration of the solar sail in the direction of the reflected photons, making reflection far more efficient for propulsion than absorption.

A solar sail made from an absorbent material will not accelerate at the same rate as a highly reflective solar sail. Compare with reason, the acceleration of the reflective and black sail solar sails.

Comparison of Acceleration: Reflective vs. Absorptive Solar Sail1. Momentum Transfer in Reflection vs. Absorption

• Reflective Solar Sail: When photons reflect off the sail, they reverse direction. This means each photon undergoes a momentum change of 2p (from −p to +p).

• Absorptive (Black) Solar Sail: When photons are absorbed, they stop moving, meaning their momentum change is only p (from −p- 0)

Thus, the momentum transferred to a reflective sail is twice as much as that transferred to an absorptive sail.

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2. Force Exerted on the Sail

Since force is the rate of change of momentum:

F=Δp/Δt

• Reflective Sail: Since Δp=2p, the force exerted is twice as large as for an absorptive sail.

• Black Sail: Since Δp = p, the force is half that of a reflective sail.

This means the reflective sail experiences double the force compared to the black sail.

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3. Acceleration Comparison

Using Newton’s Second Law:

F = ma

• Since the force on the reflective sail is twice as large, its acceleration is also twice as large as that of the black sail.

Thus, a highly reflective sail accelerates twice as fast as an absorptive (black) sail of the same mass.

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Conclusion

A reflective solar sail accelerates faster than an absorptive solar sail because reflection doubles the momentum transfer, leading to twice the force and therefore twice the acceleration. This is why solar sails are designed to be highly reflective to maximize propulsion in space