It has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil. We have to determine the size of the sail if the radiation force is to be equal in magnitude to the Sun’s gravitational attraction. We may assume that the mass of the ship + sail is 1650 kg and that the sail is perfectly reflecting, and that the sail is oriented at right angles to the Sun’s rays.
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Solution: Click For PDF Version We will use the following astronomical data for answering this problem:
Mass of the
Sun,
Rate of
energy emission from the Sun,
Let the spaceship be at a distance R (m) from the Sun. The mass of the spaceship plus that of the sails m is 1650 kg. Therefore, the gravitational pull of the Sun on the space ship will be
Let the area
of the sails be
where I is the intensity of the solar radiation at the spaceship. It will be
Therefore,
Size of the sail A is to be fixed by requiring that the magnitude of the gravitational pull of the Sun on the spaceship and that of the radiation pressure be equal. That is
This condition fixes the value of A. We have
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,
.
.
As the sails are perfectly reflecting the force experienced by the
spaceship due to the radiation pressure will be
.
.