b$.$ The helium line at $587\mathrm{.}6nm$ is present in the absorption spectrum of a star. The observed wavelength of the line varies between $586\mathrm{.}5nm$ and $588\mathrm{.}7nm$ with a period of several days.

i$.$ Explain, without calculation, what the variation in wavelength suggests about the nature of the star.

$[3$ marks$]$

ii$.$ Calculate, relative to the Earth, the maximum velocity of the star along the line of sight. $[2$ marks$]$

c$.$ The spectrum of the star has a maximum intensity at a wavelength of $340nm.$

i$.$ Calculate the surface temperature of the star. Assume that the star radiates as a black body.

$[1$ mark$]$

The parallax angle of the star is $6\mathrm{.}5{10}^{-3}$ arc$-$second.

ii$.$ Calculate, in light years $($ly$),$ the distance to the star.

$[2$ marks$]$

The apparent brightness of the star is also measured.

iii. State what is meant by apparent brightness.

$[1$ mark$]$

iv$.$ Explain, without calculation, how the radius of the star can be determined from these data.

$[3$ marks$]$

d$.$ Kepler deduced his laws of orbital motion by analysing observations of the planets in the Solar System.

i$.$ Discuss why these same laws can be applied to orbital motion of objects outside the Solar System.

$[2$ marks$]$

Astronomers have discovered many planets orbiting stars other than the Sun. The orbital periods have been directly measured for some of these planets.

ii$.$ Outline how Kepler's laws can be used to determine the orbital radii of these planets.

$[2$ marks$]$

Question $3$

a$.$ State what is meant by an elastic collision. $[1$ mark$]$

b$.$ Two stones collide on a horizontal frictionless ice surface. Stone $A,$ of mass $0\mathrm{.}10kg,$ moving with a velocity of $1\mathrm{.}6m{s}^{-1}$ hits stone $B$ of mass $0\mathrm{.}20kg$ that is initially at rest. After the collision, A moves with a velocity of $1\mathrm{.}0m{s}^{-1}$ at an angle of $60$ to the original direction of motion.

i$.$ Calculate the magnitude of the momentum of $B$ after the collision.

$[2$ marks$]$

The stones are in contact for a time of $4\mathrm{.}0{10}^{-4}s.$

ii$.$ Estimate the average force between the stones during the collision.

$[2$ marks$]$

iii. Determine whether the collision is elastic. $[2$ marks$]$ The collision of two stones is an analogue of Compton scattering. In a Compton scattering experiment, a monochromatic beam of $x-$rays is incident on a graphite target. Scattered X$-$rays are observed at an angle of $60$ relative to the direction of the incident beam.