Kleppner-Mechanics Solar sail 2

[MARX]

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*R_E
Help is greatly appreciated as solutions suggest a due to sun photon influx in towards the sun as my understanding should be away!

 

[haruspex]

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

 

[MARX]

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

 

[haruspex]

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.

 

[MARX]

I think I got it. Sun behind Earth pushing away (a_rad) and g_earth pulling closer then solve for where they balance right?

 

[MARX]

Did it that way and got right answer thanks so much for your continued help!

 

[haruspex]

I think I got it. Sun behind Earth pushing away (a_rad) and g_earth pulling closer then solve for where they balance right?

Right

 

[MARX]

Right

Thanks