Doppler effect: calculate speed of a moving star

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1. Dec 23, 2017

Pushoam

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

When the source is not moving, $\lambda = 6250 A$ .....(1)

When the source is moving, $\lambda ' = 6500 A$ .....(2)

From (1) and (2),

$\lambda ' > \lambda$ .....(3)

This means that the source is moving away from the Earth.

$\nu ' = \nu \sqrt{ \frac { c+v}{c-v}$

${\frac { \lambda }{\lambda '} }^2 = { \frac { c+v}{c-v}$

0.9245c –c = v(1+0.9245)

V =11760 km/s

Is this correct?

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2. Dec 23, 2017

Orodruin

Staff Emeritus
I hope you meant to write c - 0.9245c in the left-hand side. Otherwise the argumentation and the result seem fine.

3. Dec 23, 2017

Pushoam

I meant to write the following:
The following is wrong:
The speed v is negative implying that the star is moving away from the Earth.
v = - 11760 km/s

4. Dec 23, 2017

Pushoam

$\nu ' = \nu \sqrt{ \frac { c+v}{c-v}}$
${\frac { \lambda }{\lambda '} }^2 = { \frac { c+v}{c-v} }$

5. Dec 23, 2017

Orodruin

Staff Emeritus
Speed can never be negative as it is the absolute value of velocity. Whether the velocity is negative or not depends on which direction you defined as positive.

6. Dec 23, 2017

Pushoam

I had the impression that speed is a scalar quantity, which can be either positive or negative.
Now, I got to know that speed is defined as magnitude of velocity.

Then $\vec v = v \hat v$ where $\hat v$ is a positive constant unit vector and v could be either positive or negative and it has no specific name.
So, the following is wrong.
The correct one is :
v is negative implying that the star is moving away from the Earth.
v = - 11760 km/s

7. Dec 23, 2017

Orodruin

Staff Emeritus
If you defined the positive direction to be moving towards the star, yes. Rounding the speed gives you one of the available answers.