Respuesta :
Answer:
A. v = 2,480 10⁶ m / s , The start away us
B. v = 4.96 105 m / s, The Star moves away
C. v = -1.48 10⁶ m / s , The star is approaching
D. v = -3.43 10⁶ m / s, The star is approaching
Explanation:
This variation in the wavelength of the light emitted by the Star is explained by the relativistic Doppler effect.
f’ = √[(1+ v / c) / (1-v / c)] f
The speed of light is
c = λ f
f = c / λ
We replace
c / λ’= √ [(1+ v / c) / (1-v / c)] c /λ
Let's clear the speed, calling
β = v / c
1 / λ'² = [(1+ β) / (1 -β)] 1 /λ²
(1 -β) = (1+ β) λ'² / λ²
β (λ'² / λ² +1) = 1 - λ'² /λ²
β = [(1-λ'² /λ²) / (1 + λ'² / λ²)]
v / c = [(1 -λ'² /λ²) / (1 + λ'² / λ²)]
v = c [(1 -λ'² /λ²) / (1 + λ'² / λ²)]
Now we can solve case house
To make the calculation easier, let's call a= λ'/ λ
v = c [(1- a²) / (1 + a²)]
A) λ = 121.6 nm
λ’= 120.6 nm
Let's replace
a² = (120.6 / 121.6)²
a² = 0.9836
v = c [(1- 0.9836) / (1 + 0.9836)]
v = 3 10⁸ 8.2678 10⁻³
v = 2,480 10⁶ m / s
The start away us
B) λ‘= 121.4 nm
a² = (121.4 / 121.6)²
a² = 0.9967
v = c [(1- 0.9967) / (1 + 0.9967)]
v = 3 10⁸ 1.6527 10⁻³
v = 4.96 105 m / s
The Star moves away
C) λ’= 122.2 nm
a² = (122.2 /121.6)²
a² = 1.00989
v = c [(1- 1.00989) / (1 + 1.00989)]
v = 3 10⁸ (- 4.9207 10⁻³)
v = -1.48 10⁶ m / s
The star is approaching
D) λ’= 123.0 nm
a² = (123.0 / 121.6)²
a² = 1.02316
v = c [(1- 1.02316) / (1+ 1.02316)]
v = 3 10⁸ (-1.1447 10⁻²)
v = -3.43 10⁶ m / s
The star is approaching
