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A small space yacht, mass 9.15X10' kg, is passing hear a large star wnen Iits englnes suddenly fall. To propel the ship, the crew erects a square white sall, 6.68 km on a side, and turn it so the photons from the star hit the sail head-on. At their current distance, the solar constant (the energy that passes through 1 m² every second) is 2.89x104 w/m2. (NOTE: just as a comparison, near the Earth the solar constant is 1350 W/m2. The solar constant has the value given around the distance of Mercury from the Sun). Assume: - the sail is totally reflective; all the photons that strike the surface rebound at the same speed - the light from this star is basically monochromatic (that is, the majority of the light has one frequency) Find the acceleration achieved by the spaceship, in m/s2. Is this practical?

A small space yacht, mass 9.15X10' kg, is passing hear a large star wnen Iits englnes suddenly fall. To propel the ship, the crew erects a square white sall, 6.68 km on a side, and turn it so the photons from the star hit the sail head-on. At their current distance, the solar constant (the energy that passes through 1 m² every second) is 2.89x104 w/m2. (NOTE: just as a comparison, near the Earth the solar constant is 1350 W/m2. The solar constant has the value given around the distance of Mercury from the Sun). Assume: - the sail is totally reflective; all the photons that strike the surface rebound at the same speed - the light from this star is basically monochromatic (that is, the majority of the light has one frequency) Find the acceleration achieved by the spaceship, in m/s2. Is this practical?

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A small space yacht, mass 9.15x104 kg, is passing near a large star when its engines suddenly fail. To propel the ship, the crew erects a square white sail, 6.68 km on a side, and turn it so the photons from the star hit the sail head-on. At their current distance, the solar constant (the energy that passes through 1 m2 every second) is 2.89x104 W/m². (NOTE: just as a comparison, near the Earth the solar constant is 1350 W/m2. The solar constant has the value given around the distance of Mercury from the Sun). Assume: - the sail is totally reflective; all the photons that strike the surface rebound at the same speed - the light from this star is basically monochromatic (that is, the majority of the light has one frequency) Find the acceleration achieved by the spaceship, in m/s2. Is this practical?
Transcribed Image Text:A small space yacht, mass 9.15x104 kg, is passing near a large star when its engines suddenly fail. To propel the ship, the crew erects a square white sail, 6.68 km on a side, and turn it so the photons from the star hit the sail head-on. At their current distance, the solar constant (the energy that passes through 1 m2 every second) is 2.89x104 W/m². (NOTE: just as a comparison, near the Earth the solar constant is 1350 W/m2. The solar constant has the value given around the distance of Mercury from the Sun). Assume: - the sail is totally reflective; all the photons that strike the surface rebound at the same speed - the light from this star is basically monochromatic (that is, the majority of the light has one frequency) Find the acceleration achieved by the spaceship, in m/s2. Is this practical?
Expert Solution
Step 1

Concept used:

Photons strike the surface at speed of light to propel and basic kinematics is used.

Step 2

Given data:

  • Mass, m=9.15×104 kg
  • side of square sail, l=6.68×103 m
  • Solar constant, s=2.89×104 W/m2
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