Astrophysics

Question 1

Light or freely moving objects follow a particular path in spacetime. What is this path called?

Answer 1

Geodesic

Question 2

By referring to ‘frames of reference’, in which situations would the following apply?

a) Special relativity

and

b) General relativity

Answer 2

a) Special relativity deals with motion in inertial (non-accelerating) frames of reference.
b) General relativity deals with motion in non-interial (accelerating) frames of reference.

Question 3

When stars fuse hydrogen into helium via the proton-proton chain, which two particles are emitted during the fusion reaction?

Answer 3

positron and neutrino

Question 4

What is the unit of luminosity?

Answer 4

watts (W)

Question 5

What is meant by a conservative field?

Answer 5

The path taken between two points in the field does not affect the work done (energy) used

Question 6

On a spacetime diagram, what is the name given to lines representing an object’s motion?

Answer 6

World-lines

Question 7

Which two quantities does the luminosity of a star depend on?

Answer 7

The luminosity of a star depends on its radius and surface temperature

Question 8

In this simplified Hertzsprung-Russell diagram, which types of stars can be found in areas A, B, C and D?

Answer 8

A- Main sequence stars

B- (Red) Giants

C- (Red) Supergiants

D- White dwarfs

Question 9

What is the definition of escape velocity?

Answer 9

The minimum velocity required to allow a mass to escape a gravitational field to infinity (and have zero gravitational potential energy)

or

The minimum velocity required to allow a mass to reach infinity

Question 10

Explain the stages of high mass star’s evolution from when it leaves the main sequence until its eventual fate.

Answer 10

• Higher mass stars can fuse elements in stages all the way up to Iron.
• These stars produce so much thermal pressure that they move into the supergiant region of the HR diagram.
• When fusion stops, the star’s core collapses suddenly, and rebounds outwards as a violent supernova explosion.
• The remaining core is so dense that it becomes a neutron star or black hole.

Question 11

Describe the effect a mass has on spacetime.

Answer 11

Mass **curves **spacetime.

Question 12

What is the unit of apparent brightness?

Answer 12

watts per square metre (Wm^-2)

Question 13

What is the definition of gravitational potential, at a point in space?

Answer 13

The work done in moving a unit mass from infinity to that point in space.

Question 14

What is the definition of the gravitational field strength at a point?

Answer 14

The force exerted per unit mass (by a gravitational field).

Question 15

Describe the effect of placing a clock at a lower altitude in a gravitational field.

Answer 15

The clock would run slower at low altitude - gravitational field is stronger and so curves spacetime more.

Question 16

What is meant by the Schwarzschild radius of a black hole?

Answer 16

The Schwarzchild radius is the radius of a spherical mass where the escape velocity from the surface is equal to the speed of light.

OR

The Schwarzschild radius of a black hole is the distance from its centre (singularity) to its event horizon.

Question 17

While in the main sequence for the majority of its lifetime, explain how a star remains stable.

Answer 17

The thermal pressure outward produced by fusion is balanced by gravitational attraction.

This is called gravitational equilibrium.

Question 18

Explain the stages of a low to medium mass star’s evolution from when it leaves the main sequence until its eventual fate.

Answer 18

• Low to medium mass stars will stop fusing H to He, their cores will contract due to gravity and will start fusing He into heavier elements such as C and O.
• They will then move into the giants region of the HR diagram.
• When He fusion stops, the outer layers drift off to become a planetary nebula.
• This leaves behind a hot, dense core known as a white dwarf.

Question 19

What is the unit of gravitational potential?

Answer 19

Joules per kilogram (J kg^-1)

Question 20

State what is meant by the ‘equivalence principle’.

Answer 20

It is impossible to tell the difference
between the effects of a uniform gravitational field and
of a constant acceleration.

OR

There is no experiment that can be performed that can distinguish between the effects of a uniform gravitational field and constant acceleration.

Question 21

The world-lines on the following space time diagram represent the motion of different objects, A, B and C.

Describe the motion of objects A, B and C.

Answer 21

Object A is stationary

Object B is moving with a constant velocity

Object C is accelerating

Question 22

How would you convert between

1. astronomical units (AU) and metres?
2. light years and metres?

Answer 22

1. 1 AU = 1.5 x 10¹¹ m (given in data sheet)
2. 1 light year = 3 x 10⁸ x 365.25 x 24 x 60 x 60 (= 9.46 x 10¹⁵ m) (NOT in data sheet!)

Question 23

Derive the expression shown below for escape velocity.

Answer 23

E_k + E_p = 0

½mv² + (-GMm/r) = 0

½mv² = GMm/r

v² = 2GM/r

v = √2GM/r

Question 24

Shown is the relationship used to find the gravitational potential at a point in space.

How could you find the gravitational potential energy of a mass, m, at that point?

Answer 24

Multiply the gravitational potential by the mass:

E_p = V x m

Question 25

Which quantity of a star determines its ultimate fate?

Answer 25

Its mass.

Question 26

Describe the effect of placing a clock at a higher altitude in a gravitational field.

Answer 26

The clock would run faster at high altitude - gravitational field is weaker and so curves spacetime less.

Question 27

What is the value of a field’s gravitational potential at infinity?

Answer 27

At infinity, the gravitational potential of a field is zero.

Question 28

What is the main change in the fusion reactions of a star when it leaves the main sequence?

Answer 28

Nuclear fusion of hydrogen will cease in the core of the star.

Question 29

Describe the fusion reactions happening in a main sequence star.

Answer 29

Fusion of hydrogen occurs in the core of main sequence stars.

Question 30

Every star ultimately becomes a white dwarf, a neutron star, or a black hole.
Which one of these will our Sun become?

Answer 30

White dwarf
(our Sun is a low-mass star)