One possible means of achieving space flight is to place a...

One possible means of achieving space flight is to place a perfectly reflecting aluminized sheet into Earth’s orbit and to use the light from the Sun to push this solar sail. Suppose such a sail, of area $6.00 \times 10^{4} \mathrm{m}^{2}$ and mass $6.00 \times 10^{3} \mathrm{kg}$ is placed in orbit facing the Sun. (a) What force is exerted on the sail? (b) What is the sail’s acceleration? (c) How long does it take this sail to reach the Moon, $3.84 \times 10^{8} \mathrm{m}$ away? Ignore all gravitational effects and assume a solar intensity of 1340 $\mathrm{W} / \mathrm{m}^{2}$ Hint: The radiation pressure by a reflected wave is given by 2 (average power per unit area)/c.

Key Concepts

Kinematics Under Constant Acceleration

When an object is acted upon by a constant net force, its motion can be described by the kinematic equations of motion. These equations are used to calculate quantities such as displacement and time, which are crucial for understanding how long it would take a continuously accelerating solar sail to travel a specified distance, such as the distance to the Moon.

Radiation Pressure

Radiation pressure is the pressure exerted by light or other electromagnetic radiation on surfaces due to the momentum carried by photons. It becomes especially significant in contexts like solar sails, where the force generated by this pressure, though small compared to conventional mechanical forces, can accumulate over time to produce measurable acceleration in space.

Momentum Transfer Through Reflection

When electromagnetic waves are reflected, the change in momentum is effectively doubled compared to absorption. This concept is key in the functioning of solar sails because a perfectly reflecting surface, like that proposed for the sail, maximizes the force generated by the incident sunlight, making it more efficient as a propulsion system.

Newton's Second Law

Newton's Second Law, which states that force equals mass times acceleration (F = ma), is fundamental in relating the calculated force from radiation pressure to the resulting acceleration of the solar sail. This law allows one to determine how a given continuous force will affect the velocity of an object over time.

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