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3 years ago

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On average, how many stars would we have to search before we would expect to hear a signal? assume there are 500 billion stars i

n the galaxy.

1 answer:

Keith_Richards [23]3 years ago

7 0

We would have to search at least 5,000,000,000 (5 billion) stars before we would expect to hear a signal.

To find out the number of stars that we will need to search to find a signal, we need to use the following formula:

total of stars/civilizations
500,000,000,000 (500 billion) stars / 100 civilization = 5,000,000,000 (5 billion)

This shows it is expected to find a civilization every 5 billion stars, and therefore it is necessary to search at least 5 billion stars before hearing a signal from any civilization.

Note: This question is incomplete; here is the complete question.

On average, how many stars would we have to search before we would expect to hear a signal? Assume there are 500 billion stars in the galaxy.

Assuming 100 civilizations existed.

Learn more about stars in: brainly.com/question/2166533

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Explanation:

Given

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The required speed so that it does not take more than 70 years is then calculated using:

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So, we have:

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$\triangle x'^2 = \frac{v^2T^2_0}{1 - v^2/c^2}$

Cross Multiply

$(1 - \frac{v^2}{c^2}) *\triangle x'^2 = v^2T^2_0$

Divide both sides by $\triangle x'^2$

$(1 - \frac{v^2}{c^2}) = \frac{v^2T^2_0}{\triangle x'^2}$

Divide through by $v^2$

$(\frac{1}{v^2} - \frac{v^2}{v^2*c^2}) = \frac{v^2T^2_0}{v^2\triangle x'^2}$

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Make $\frac{1}{v^2}$ the subject

$\frac{1}{v^2} = \frac{T^2_0}{\triangle x'^2} + \frac{1}{c^2}$

Inverse both sides

$v^2 = \frac{1}{\frac{T^2_0}{\triangle x'^2} + \frac{1}{c^2}}$

Take square root of both sides

$v = \sqrt{\frac{1}{\frac{T^2_0}{\triangle x'^2} + \frac{1}{c^2}}}$

Substitute values for $T_0$ and $\triangle x$

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$v = \sqrt{\frac{1}{\frac{70^2}{70^2*c^2} + \frac{1}{c^2}}}$

$v = \sqrt{\frac{1}{\frac{1}{c^2} + \frac{1}{c^2}}}$

$v = \sqrt{\frac{1}{\frac{2}{c^2}}}$

$v = \sqrt{\frac{c^2}{2}}$

$v = c\sqrt{\frac{1}{2}}$

$v = c * 0.7071$

$v = 0.7071c$

7 0

3 years ago