# Gravitational Waves: scale of the phenomenon

### Problem 1: Athletic challenge

A world champion in sprint starts the race. Estimate the portion of energy he spends that goes into production of gravitational waves.

### Problem 2: Spinning dumb-bell

Imagine a dumb-bell consisting of two 1-ton compact masses with their centers separated by 2 meters and spinning at 1 kHz about a line bisecting and orthogonal to their symmetry axis.Estimate the amplitude of gravitational waves at the distance of $r=300km$ from this source

### Problem 3: Supernova explosion

Estimate the amplitude of the gravitational wave produced by a supernova explosion in our Galaxy.

### Problem 4: Pulsar binary

Consider a pair of $1.4{M}_{\odot}$ neutron stars $15Mpc$ away (e.g., near the center of the Virgo galactic cluster) on a circular orbit of $20km$ radius and orbital frequency of $400Hz$. Estimate the amplitude of gravitational wave.

### Problem 5: Neutron star mergers

Estimate the energy flux of gravitational waves, registered on Earth, from a pair of merging neutron stars in the Virgo cluster with the same parameters. Compare with the energy flux from the Sun.

### Problem 6: The Jovian generator

In the Solar system the most considerable source of gravitational waves is the subsystem of Sun and Jupiter. Estimate its power.

### Problem 7: Gravity in atom

Estimate the lifetime of the hydrogen atom in the $3d$ state with respect to decay into $1s$ due to gravitational (as opposed to electromagnetic) interaction, and emission of a graviton.