Question

A possible means of space flight is to place a perfectly reflectingaluminized sheet into orbit around the Earth and then use the lightfrom the Sun to push this "solar sail." Suppose a sail of area5.00 105 m2 and mass 6300 kg is placed in orbit facing the Sun.

(a) What force is exerted on the sail?
N
(b) What is the sail's acceleration?
m/s2
(c) What time interval is required for the sail to reach the Moon,3.84 multiplied by 108 maway? Ignore all gravitational effects, assume the accelerationcalculated in part (b) remains constant, and assume a solarintensity of 1370 W/m2.
days

Answer 1

a) F = 4.57 N, b) a = 0.725 m / s² , c) t = 3,254 10⁴ s

Step-by-step explanation:

a) for this problem let's start by using the radiation pressure for a reflective surface

P = 2 S / c

The definition of pressure is

P = F / A

F / A = 2S / c

F = 2 S A / c

F = 2 1370 5.00 105/3 108

F = 4.57 N

b) The acceleration can be calculated with Newton's second law

F = m a

a = F / m

a = 4.57 / 6300

a = 0.725 m / s²

c) the time to reach the Moon, suppose the trip is in a straight line, therefore the initial speed towards the Moon is zero

y = vo t + ½ a t²

y = ½ a t²

t = √ 2y / a

t = √ (2 3.84 10⁸ /0.725)

t = 3,254 10⁴ s