35. Special Relativity

We cannot use Hubble’s law to measure the distances to nearby galaxies, because their random motions are larger than the overall expansion. Indeed, the closest galaxy to us, the Andromeda Galaxy, 2.5 million light-years away, is approaching us at a speed of about 130km/s. (a) What is the shift in wavelength of the 656-nm line of hydrogen emitted from the Andromeda Galaxy, as seen by us? (b) Is this a redshift or a blueshift? (c) Ignoring the expansion, how soon will it and the Milky Way Galaxy collide?

Calculate the speed of a proton (m = 1.67 x 10^-27 kg) whose kinetic energy is exactly half its total energy.

Suppose a spacecraft of mass 17,000 kg was accelerated to 0.22c.

(a) How much kinetic energy would it have?

(b) If you used the classical formula for kinetic energy, by what percentage would you be in error?

The quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per 1 m/s increase in speed. A 25,000 kg rocket is traveling at 0.90c. How much additional energy is needed to increase its speed by 1 m/s?

The half-life of a muon at rest is 1.5 μs. Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of 7.5 μs. What is the total energy of a muon in the storage ring? The mass of a muon is 207 times the mass of an electron.

At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?

The sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. What percent is this of the sun's total mass?

The sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.