Consider a large solar sail in the form of a square with sides of length e = 100 m that is fabricated from a stiff, completely transparent plastic sheet. To make the sail more rigid the plastic sheet is bent back and forth along a series of equispaced lines parallel to one edge thereby forming a "concertina-like" structure as shown in the figure. The distance, d, between the bends is d << l and the angle at each bend is 90°. a) If the front face of the sail has a highly reflective coating deposited on it and the sail is illuminated normally with radiation of intensity I = 1.3 kW m², determine the total radiative force experienced by the sail. b) If over time the reflective coating degrades such that it only reflects 50% of the incident radiation, the remaining 50% being transmitted through the plastic sheet, what is the radiative force now experienced by the sail? l=100m c) How is the answer to part b) changed if the plastic sheet has also degraded such that it is no longer completely transparent but absorbs 30% of the radiation attempting to pass through it? [Note - all dimensions in this problem are very much larger than the wavelength of the incident radiation.]

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**Solar Sail Problem**

Consider a large solar sail in the form of a square with sides of length \( \ell = 100 \ \text{m} \) that is fabricated from a stiff, completely transparent plastic sheet. The plastic sheet is bent back and forth along a series of equally spaced lines parallel to one edge, forming a "concertina-like" structure as shown in the figure. The distance, \( d \), between the bends is \( d \ll \ell \) and the angle at each bend is \( 90^\circ \).

a) If the front face of the sail has a highly reflective coating and the sail is illuminated normally with radiation of intensity \( I = 1.3 \ \text{kW m}^{-2} \), determine the total radiative force experienced by the sail.

b) If over time the reflective coating degrades such that it only reflects 50% of the incident radiation, with the remaining 50% transmitting through the plastic sheet, what is the radiative force now experienced by the sail?

c) How is the answer to part b) changed if the plastic sheet has also degraded such that it is no longer completely transparent but absorbs 30% of the radiation attempting to pass through it?

**Note:** All dimensions in this problem are significantly larger than the wavelength of the incident radiation.

**Diagram Explanation**

The diagram depicts a zigzag pattern representing how the plastic sheet is folded. The vertical lines with arrows show the direction of the incident radiation. It highlights the concertina-like structure and labels the distance between the folds as \( d \) and the length of each side of the square as \( \ell = 100 \ \text{m} \).
Transcribed Image Text:**Solar Sail Problem** Consider a large solar sail in the form of a square with sides of length \( \ell = 100 \ \text{m} \) that is fabricated from a stiff, completely transparent plastic sheet. The plastic sheet is bent back and forth along a series of equally spaced lines parallel to one edge, forming a "concertina-like" structure as shown in the figure. The distance, \( d \), between the bends is \( d \ll \ell \) and the angle at each bend is \( 90^\circ \). a) If the front face of the sail has a highly reflective coating and the sail is illuminated normally with radiation of intensity \( I = 1.3 \ \text{kW m}^{-2} \), determine the total radiative force experienced by the sail. b) If over time the reflective coating degrades such that it only reflects 50% of the incident radiation, with the remaining 50% transmitting through the plastic sheet, what is the radiative force now experienced by the sail? c) How is the answer to part b) changed if the plastic sheet has also degraded such that it is no longer completely transparent but absorbs 30% of the radiation attempting to pass through it? **Note:** All dimensions in this problem are significantly larger than the wavelength of the incident radiation. **Diagram Explanation** The diagram depicts a zigzag pattern representing how the plastic sheet is folded. The vertical lines with arrows show the direction of the incident radiation. It highlights the concertina-like structure and labels the distance between the folds as \( d \) and the length of each side of the square as \( \ell = 100 \ \text{m} \).
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