Kleppner-Mechanics Solar sail 2

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    Solar Solar sail
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The discussion revolves around the design of a solar sail capable of achieving escape velocity from Earth using sunlight pressure. Participants address the calculations for acceleration due to sunlight and the necessary distance from Earth for the sail to escape its gravitational pull. Confusion arises regarding the influence of the Sun's gravity and photon pressure, with some contributors clarifying that the focus should be solely on escaping Earth's gravity. The correct approach involves considering the balance of forces between the Earth's gravitational pull and the sunlight pressure. Ultimately, the participants arrive at the correct solution by properly positioning the Sun in relation to the Earth.
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Homework Statement


  1. 4.18
    With reference to Example 4.21, consider the design of a solar sail

    intended to reach escape velocity from the Earth 2gRe = 11.2 km/s using only the pressure due to sunlight. The sail is made of a Kapton⃝R film 0.0025 cm thick with a density 1.4 g/cm3. Take the solar constant to be 1370 watts/m2, assumed to be constant during the acceleration.

    (a) What is the acceleration near the Earth due to sunlight pres- sure alone?

    (b) How far from the Earth, as measured in units of the Earth’s radius, Re, would the sail have to be launched so that it could es- cape from the Earth?

Homework Equations


attached

The Attempt at a Solution


Solution attached
no issues with part a
part b: I am getting the wrong answer as solution come up with r ≥ 194*RE
Help is greatly appreciated as solutions suggest a due to sun photon influx in towards the sun as my understanding should be away!
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Judging from your diagram for part b, you have not understood the question. You seem to have found the point between Earth and Sun where the two gravitational forces and the photon pressure would balance.
Forget the Sun's gravity; it is a question about escaping Earth's gravitational field
 
ok I did think doing it that way. But if both accelerations are towards the earth, how can it ever escape! Unless a of photons is coming in from the Earth not the sun? But how? light is coming from the sun photon influx. Still totally confused. Thanks for helping
 
MARX said:
But if both accelerations are towards the earth,
perhaps you have the wrong diagram. Start with the sail and the Earth, then position the sun.
 
I think I got it. Sun behind Earth pushing away (arad) and gearth pulling closer then solve for where they balance right?
 
Did it that way and got right answer thanks so much for your continued help!
 
MARX said:
I think I got it. Sun behind Earth pushing away (arad) and gearth pulling closer then solve for where they balance right?
Right
 
haruspex said:
Right
Thanks
 

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