# Search

astrophysics (83)biophysics (18)chemistry (21)electric field (69)electric current (73)gravitational field (79)hydromechanics (141)nuclear physics (42)oscillations (55)quantum physics (31)magnetic field (41)mathematics (88)mechanics of a point mass (290)gas mechanics (86)mechanics of rigid bodies (219)molecular physics (71)geometrical optics (77)wave optics (65)other (163)relativistic physics (37)statistical physics (21)thermodynamics (149)wave mechanics (51)

## astrophysics

### (10 points)6. Series 34. Year - P. more dangerous corona

When there is a coronal mass ejection from the Sun, the mass will start to propagate with high velocity through the space. Sometimes the mass can hit the Earth and affect its magnetic field. Estimate the magnitude of the electric currents in the electric power transmission network on Earth which could be generated by such ejection. What parameters does it depend on? Comment on what effects would such event have on the civilisation.

Karel was at a conference and then he saw a video on the same topic.

### (3 points)5. Series 34. Year - 2. retarded Jupiter

The sidereal period of Jupiter is approximately $11,9 \mathrm{years}$, the speed of light is $3 \cdot 10^{8} \mathrm{m\cdot s^{-1}}$. Assume the relative distance between the Earth and the Sun to be $150 \cdot 10^{9} \mathrm{m}$. Using these values, calculate how long will the light travel from Jupiter to Earth if Jupiter is located at a point to which it will get from opposition in one quarter of the sidereal period.

Vašek remembered the observations of Ole R\o {}mer.

### (8 points)4. Series 34. Year - 5. Efchári-Goiteía

Efchári and Goiteía are two components of a double planet around recently arisen stellar system. They orbit around a common centre of mass on circular trajectories in the distance $a = 250 \cdot 10^{3} \mathrm{km}$. Efchári has the radius $R_1 = 4~300 km$, density $\rho _1 = 4~100 kg.m^{-3}$ and siderial period $T_1 = 14 \mathrm{h}$. Goiteía is smaller – it has the radius $R_2 = 3~800 km$, but it has a higher density $\rho _2 = 4~500 kg.m^{-3}$ and a shorter period $T_2 = 11 \mathrm{h}$. Rotation axes of both planets and the system are parallel. After several hundred years, the system transfers due to tidal forces into so-called tidal locking. Find the resulting difference in the period of the system, assuming that both bodies are homogeneous and roughly spherical.

Dodo keeps confusing Phobos and Deimos.

### (6 points)3. Series 34. Year - 3. kaboom, kaboom

Imagine placing a large number of satellites on the geosynchronous orbit. Coincidentally, a runaway series of collisions occurs and forms a thin spherical layer homogenously scattered with ten million shards with an average size of $x = 10 \mathrm{cm}$. Assume that the velocity directions of the individual shards are oriented randomly in the plane tangent to the sphere. On average, how much time passes between two collisions?

Dodo learned about transport phenomena in gasses for his state exams.

### (3 points)2. Series 34. Year - 1. there is light -- there is none

The length of daytime and nighttime varies during the year and it may vary differently in different places on Earth. What about the average length of daytime during one year? Is it the same everywhere or does it vary in different places? A qualitative description is sufficient.

**Bonus:** Try to estimate the maximum difference between the average length of daytime and $12 \mathrm{h}$.

Dodo was discarding old problems.

### (10 points)6. Series 33. Year - S.

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

### (3 points)4. Series 33. Year - 1. tchibonaut

Consider an astronaut of weight $M$ remaining still (with respect to a space station) in zero-g state, holding a heavy tool of weight $m$. The distance between the astronaut and the wall of the space station is $l$. Suddenly, he decides to throw the tool against the wall. Find his distance from the wall when the tool hits it.

Karel wanted to set this name for this problem.

### (10 points)4. Series 32. Year - P. V-1 in the space

The interstellar space is not empty but contains an insignificant amount of mass. For simplicity, assume hydrogen only and look up the required density. Could we build a spaceship that would „suck in“ the hydrogen and would use energy from it? How fast/large would the spaceship have to be in order to keep up the thermonuclear fusion only from the acquired hydrogen? What reasonable obstacles in realization should we consider?

crypto-facism → Red Dwarf → drive → thrust → V-1 and the circle closes

### (12 points)1. Series 32. Year - E. hourly

Measure the length of one day. However, there is a limitation: one continuous measurement can't take longer than one hour. For the sake of statistical accuracy, though, do repeat your measurements multiple times.

Jachym had an hour until deadline

### (10 points)1. Series 32. Year - P. terrible cold

Some nebulas constituted of a gas from stars, e. g. Bumerang, have lower temperature than the Cosmic Microwave Background (CMB), hence are technically colder than space. How is this possible? Try to determine a condition for a gas ejected by a hot star to cool down below the temperature of the CMB.

Karel wasn't satisfied with the claim that the temperature everywhere in space is at least that of the CMB.