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kow [346]
4 years ago
10

As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phase

s of the moon describe how much of the surface appears to be in sunlight. An astronomical measure of phase is given by the fraction F of the lunar disc that is lit. When the angle between the sun, the earth, and the moon is θ(0<=θ<=360∘), then
F=1/2(1−cosθ)
Determine the angles θ, that correspond to the following phases:

(a) F = 0 (new moon)
(b) F = 0.25 (a crescent moon)
(c) F = 0.5 (first or last quarter)
(d) F = 1 (full moon)
Mathematics
1 answer:
lys-0071 [83]4 years ago
7 0

Answer:

a)   0∘ and  360∘

b)   300∘ and  60∘

c)   90∘ and  270∘

d)   180∘

Step-by-step explanation:

θ(0<=θ<=360∘)

then

a)

F=1/2(1−cosθ)

Putting F= 0

we get

0 = 1/2 (1−cosθ)

(1−cosθ) = 0

cosθ = 1

θ = cos^-^1 (1)

 = 0∘ and  360∘

b) If F = 0.25

then putting values

1/4 = 1/2 (1−cosθ)

(1−cosθ) = 1/2

cosθ = 1/2

θ = cos^-^1 (1/2)

 = 300∘ and  60∘

c) If F = 0.5

then  putting values we get

1/2 = 1/2 (1−cosθ)

(1−cosθ) = 1

cosθ = 0

θ = cos^-^1 (0)

 = 90∘ and  270∘

d) If F = 1

then  putting values we get

1 = 1/2 (1−cosθ)

(1−cosθ) = 2

cosθ = -1

θ = cos^-^1 (-1)

 = 180∘

So after these calculation we determine the vales of angles that are given uper.

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