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## astrophysics

### 2. Series 31. Year - 4. nuclear waste no more

Imagine we have a thing (e.g. a nuclear waste container) and we want to get rid of it. We transfer the object to a circular orbit around the Sun at the same distance as Earth, but far enough from Earth to ignore its gravitational influence. Which of these methods of the objects disposal would require the least amount of energy and thus would be the most efficient?

- Throw it into the Sun. Getting it to the solar surface would be sufficient to burn the object.
- Transfer it to a circular orbit in the Asteroid belt (located between the orbits of Mars and Jupiter).
- Get it out of the Solar System completely.

Karel thought about what exactly is SEO and discovered this problem.

### 1. Series 31. Year - 5. planetary colonization

You have probably already thought about whether there are alien civilizations in the universe. As a general rule, the bigger a star the higher is its radiation power and the shorter its life. Let's focus on two stars, where one has twice the power output than the other. If the band where life is possible is given by the steady state temperature of a black body orbiting there, which has a lower and upper limit (that are the same for each and every system), around which star is this life-supporting band wider? How many times larger it will be in comparison to the other star?

Karel often procrastinates on Youtube.

### 0. Series 31. Year - E.

*We are sorry. This type of task is not translated to English.*

### 6. Series 30. Year - P. evaporating asteroid

A very large piece of ice (let us say with diameter 1 km) is placed near a Sun-like star to a circular orbit. It is placed so close, that the equillibrium temperature of a black body at this distance would be approximately 30 ° C. What will happen with such an asteroid and its orbit? The asteroid is not tidally locked.

Karel likes astrophysics, so he came up with something again.

### 2. Series 30. Year - 1. beach date

Imagine you are going on a date with your girlfriend/boyfriend and you end up watching the sunset on the beach. The sun above the sea horizon looks very romantic, so to prolong this special moment, you decide to use a forklift to lift you up. The forks of the forklift move up with such speed that you can see the sun touching the horizon at any moment. Determine the speed of the forks.

Dominika vzpomínala na Itálii.

### 3. Series 29. Year - P. Lukas' hole

Lukas has been weightlifting and he managed to make a black hole of mass 1 kg. As he isn't too fond of quantum field theory in curved spacetime, the black hole does not radiate. Lukas drops this hole and it begins oscillating within the earth. Try to estimate how long would it take for the mass of the black hole to double. Is it safe to make black holes at home?

### 1. Series 29. Year - 4. the lethal lens

Imagine that around the Sun on a circular orbit is a convex lens with a diameter that is equal to the diameter of the Sun, the focal point of which orbits with a sufficient precision on the orbit of Earth. Determine how the lens will burn the Earth during one of its orbit (ie. how much solar energy will be given to Earth by the lens), if it orbits at the distance of Mercury and compare it with the state where it will be as far as Venus.

**Bonus:** Consider the eclipse that the lens will cause during its orbit.

Mirek wanted to use a lens to focus the beams from the sun during an eclipse.

### 1. Series 28. Year - P. Moon from Mars

Can you see the Moon from Mars with a naked eye.Ground your answer in calculations.

Kuba wanted to be brief.

### 3. Series 27. Year - 1. eclipse

A planet is orbiting around a star on a circular orbit and a moon is orbiting around the planet on a circular orbit in the plane of the planet's orbit. We know that, during the eclipse of the sun the angular size of the moon is the same as the angular size of the sun if observed from the surface of the planet (the moon perfectly covers the sun). Furthermore we know that the planet perfectly covers the moon during the moon's eclipse. Determine the ratio of the radius of the planet $R$ and the moon $r$, if the distance of the planet from the star is very large compared to the distance of the moon from the planet $L$ and this is in turn larger by several orders of magnitude than the dimensions $R$, $r$.

Mirek was looking through the archive.

### 2. Series 27. Year - 4. The stellar size of the Moon

It is known that the Moon when it is full has the apparent magnitude of approximately -12 mag and the Sun during the day has the apparent magnitude of -27 mag. Try to figure out what is the apparent magnitude of the Moon directly before a solar eclipse, if you know that the albedo of the Earth is approximately 0.36 and the albedo of the Moon 0.12. Presume that light after reflection disperes the same way on the surface of both the Moon and Earth.

Janči byl oslepený.