Kleppner-Mechanics Solar sail 2

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    Solar Solar sail
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Homework Help Overview

The discussion revolves around a problem from Kleppner's Mechanics concerning the design of a solar sail intended to achieve escape velocity from Earth using sunlight pressure. The problem involves calculating the acceleration due to sunlight pressure and determining the distance from Earth required for the sail to escape its gravitational influence.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the correct interpretation of the forces acting on the solar sail, particularly the balance between Earth's gravitational pull and the pressure from sunlight. There is confusion regarding the direction of forces and the implications of the solar sail's position relative to the Earth and the Sun.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have suggested reconsidering the diagram and the forces involved, while others have indicated they found a potential resolution. However, there is no explicit consensus on the correct approach yet.

Contextual Notes

Participants are grappling with the assumptions regarding the gravitational influences of both the Earth and the Sun, as well as the nature of the forces acting on the solar sail. There is mention of a specific solution that suggests a distance greater than 194 times the Earth's radius, which some participants are questioning.

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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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