For an object 1.7 times the mass of the Sun (the Sun is 1.99 × 1030 kg), work out the radius it would have if it were a

Question
Astronomy subject(This question might look long, but most of the

sentences are hints actually, I believe it should not take too much

time as these are just low points questions in my assignment)

1.)
Description:
Stars
like the Sun can be considered to be supported by gas and radiation
pressure. In other words, the star will collapse until the outward
pressure of the gas and radiation it produces balances the inward
attraction due to gravity. For a white dwarf star, which our Sun will
become once it dies, the star is instead supported by electron
degeneracy pressure. Material in a white dwarf star is incredibly
densely packed together, further collapse under the influence of gravity
is prevented by the pressure of the electrons repelling one another.
Neutron stars, which are the end result of stars more massive than the
Sun, are denser still. They are so tightly squeezed together that the
protons and electrons within them have been pushed together to form
neutrons. The collapse of a neutron star under the influence of gravity
is prevented due to neutron degeneracy pressure (caused by the strong
nuclear force).

Questions:
For an object 1.7 times the mass of the Sun (the Sun is 1.99 × 1030 kg), work out the radius it would have if it were a:

i) main sequence star, supported by gas and radiation pressure of 280 Pa m2 kg-1.
ii) a white dwarf, supported by electron degeneracy pressure of 3.6 × 106 Pa m2 kg-1.
iii) a neutron star, supported by a neutron degeneracy pressure of 9.2 × 1011 Pa m2 kg-1.

(all units in metre)
HINT:
Pressure
= Force/Area, so if you consider the force due to gravity on a 1kg
object of surface area 1 m2, and the object is in equilibrium, ie the
force due to gravity balances the force due to the pressure then
Pressure (in Pa m2 kg-1) = GM/r2.

2.)
Young white dwarfs
are typically far hotter than stars like the Sun (e.g. Twd ? 42,000K;
TSun ? 6,000 K). Despite this, they are also very, very faint. Given a
white dwarf that is seven times hotter than a star, and using the radii
(for the star and white dwarf) you calculated earlier in this question,
calculate how much brighter (or fainter) that white dwarf would be than a
star like the Sun.

L white dwarf = (Answer) ×L star ???

HINT:
L is the luminosity, the power (P) radiated by the object. Right at the
begining of the course (kettle topic) you saw that for radiation the
power is given by:
L = P = ?AeT4
in this equation e is the
emisivity (1 for the Sun and a white dwarf), ? is Stefans constant =
5.67 × 10-8 Js-1m-2K-4, A is the surface area in m2 and T is the
temperature in K.

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