Life on Mars?

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Problem 1: on intelligent aliens

Consider a highly developed alien civilization, actively exploring the Earth in search of intelligent life. How would citizens of opposite part of Milky Way see those from the Earth? And what about citizens of Andromeda galaxy?

Problem 2: homo sapiens in the Galaxy

Estimate the number of stars, which had already received the signal about homo sapiens being (existence) on the Earth.

Problem 3: the Galactic Habitable Zone

Inhabited planets in our Galaxy are likely to be located within so--called galactic habitable zone, which has a form of narrow ring with a radius greater or approximately equal to half radius of Galaxy. Explain, why genesis (?) is unlikely to happen at too small and too large galactocentric distances.

Problem 4: Habitable Zone dynamics

Why does the width of galactic habitable zone gradually increase in time?

Problem 5: the Fermi paradox

One of the possible formulations of the Fermi paradox, or the great silence paradox, is the following: if there is intelligent life in the Universe, why does it not emit any signal into space and generally manifest itself in any way? This paradox is related to the name of Fermi, because once having listened to the arguments of his colleagues stating that there is a great number of highly developed technological civilizations, he asked after some pause: So, where are they? Give arguments to support or disprove the paradox.

Fine-tuning of the Universe

Problem 6: varying electron mass

$^*$ Imagine for a moment, that electron has mass several times larger that actual. If other conditions ware the same, how would our Universe change?

Problem 7: electron mass from anthropic principle

Our Sun emits energy during billions of years and thus supports life development on the Earth. It is possible due to very slow reaction of deuteron creation from two interacting protons. Find the limiting value of electron mass providing the necessarily low rate of such reaction.