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

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

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

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

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

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

What is the definition of escape velocity?

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**

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

a) Special relativity

and

b) General relativity

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.

State what is meant by the 'equivalence principle'.

It is impossible to tell the difference

between the effects on an observer of a **uniform gravitational field **and

of a **constant acceleration**.

OR

There is no experiment that can be performed that can distinguish between being in a uniform gravitational field and undergoing constant acceleration.

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

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

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

World-lines

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

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

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.

Object A is stationary

Object B is moving with a constant velocity

Object C is accelerating

Light or freely moving objects under the influence of gravity follow particular paths in spacetime. What are these paths called?

Geodesics

Describe the effect a mass has on spacetime.

Mass curves (or distorts) spacetime.

Describe what we understand as gravity in terms of spacetime.

Gravity is caused by the curvature of spacetime. Masses follow this curvature of spacetime.

Which two quantities does the **Luminosity** of a star depend on?

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

When stars fuse hydrogen into helium via the proton-proton chain releasing energy (gamma rays) in the process, which two **other** particles are produced?

positrons and neutrinos

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

A- Main sequence stars

B- (Red) Giants

C- (Red) Supergiants

D- White dwarfs

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

###
- 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.**

**planetary nebula**.**white dwarf.**Explain the stages of high mass star's evolution from when it leaves the main sequence until its eventual fate.

###
- 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.**

**supergiant**region of the HR diagram.**supernova**explosion.**neutron star**or**black hole.**Which quantity of a star determines its ultimate fate?

Its mass.

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

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

It is in **gravitational equilibrium.**

What is the unit of gravitational potential?

Joules per kilogram (J kg^{-1})

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?

Multiply the gravitational potential by the mass:

E_{p }= V x m

Derive the expression shown below for escape velocity.

E_{k} + E_{p} = 0

½mv^{2} + (-GMm/r) = 0

½mv^{2} = GMm/r

v^{2} = 2GM/r

**v = √2GM/r**

What is the unit of Luminosity?

Watts (W)

What is the unit of apparent brightness?

Watts per square metre (Wm^{-2})

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

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.

What is meant by a conservative field?

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

How would you convert between

- astronomical units (AU) and metres?
- light years and metres?

###
- 1 AU = 1.5 x 10
^{11} m (given in data sheet)
- 1 light year = 3 x 10
^{8} x (365.25 x 24 x 60 x 60) = **9.46 x 10**^{15} m (NOT in data sheet!)

^{11}m (given in data sheet)^{8}x (365.25 x 24 x 60 x 60) =**9.46 x 10**(NOT in data sheet!)^{15}m