# Kleppner-Mechanics Solar sail 2

• MARX
In summary, the conversation discusses the design of a solar sail to reach escape velocity from Earth using only sunlight pressure. The sail is made of a Kapton⃝R film and the solar constant is assumed to be constant during acceleration. The solution for part a is correct, but there was confusion over the diagram for part b. The correct approach is to consider the balance between the acceleration from the sun's photon pressure pushing away from Earth and the Earth's gravity pulling towards it. The correct answer for the distance from Earth, measured in units of Earth's radius, is r ≥ 194*RE.

## 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?

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!

#### Attachments

• IMG_0072.JPG
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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

## What is the Kleppner-Mechanics Solar sail 2?

The Kleppner-Mechanics Solar sail 2 is a type of spacecraft that uses the radiation pressure from sunlight to propel itself through space. It is a more advanced version of the original solar sail concept proposed by Albert Einstein and relies on the principles of classical mechanics to function.

## How does the Kleppner-Mechanics Solar sail 2 work?

The solar sail is made up of a large reflective material, such as Mylar, that reflects sunlight and creates a force in the opposite direction. This force, known as radiation pressure, is what propels the spacecraft forward. The sail is also equipped with small motors that can adjust its orientation to maximize the force from the sunlight.

## What are the advantages of using the Kleppner-Mechanics Solar sail 2?

One of the main advantages of using a solar sail is that it does not require any fuel, making it a more cost-effective and environmentally friendly option for space propulsion. Additionally, it can reach much higher speeds compared to traditional spacecraft, as it is not limited by the amount of fuel it can carry.

## What are the potential applications of the Kleppner-Mechanics Solar sail 2?

The solar sail has the potential to revolutionize space exploration, as it could be used for long-distance missions, such as interstellar travel. It could also be used to maintain the position of satellites in space, reducing the need for costly fuel refills.

## What are the challenges facing the development and use of the Kleppner-Mechanics Solar sail 2?

One of the main challenges is the delicate balance between the reflective material's weight and the amount of light it can reflect. Additionally, the sail must be able to withstand the harsh conditions of space, such as extreme temperatures and debris. Deployment and control of the sail also require precise and advanced technology.