Mapping the Heavens. How Long is a Day? WILF: Be able to draw diagrams to show the phases of the moon and be able to explain what a sidereal day is. Starter:

Mapping the Heavens

How Long is a Day?

WILF: Be able to draw diagrams to show the phases of the moon and be able to explain what a sidereal day is.

Starter: True or false

1. The sun rises in the East

2. The sun comes up at the same time each day

3. The moon only comes out at night

4. The Earth goes around the sun

5. The moon goes around the sun

6. We always see the same side of the moon

7. The moon orbits the earth once a day

8. The Earth is closer to the sun in June than in December

9. The moon rotates

10. There are no stars in the daytime sky.

21 Apr 2023

Keywords:

Phases of the moon

Sidereal day

Solar day

Complete the diagram

Star is seen at midnight

Midday – sun is visible

6 hrs later12 hrs later18 hrs later23 hrs 56 minutes later24 hrs later

Star is seen at 23 hrs and 56 minMidday –

sun is visible

Sidereal Days and Solar Days

The average time it takes the sun to cross the sky is 24 hrs. This is called a solar day.

The Earth rotates through 3600 once every 23hrs and 56 minutes. A star would appear in the same position in the night sky therefore 23 hrs and 56 minutes later. This is called a sidereal day.

EclipsesKeywords:

Lunar eclipse

Solar eclipse

Shadow

Totality

Corona

Umbra

Penumbra

WILF: Be able to explain how seasons occur and why eclipses are such rare events.

Starter: the sun appears to travel across the sky once every 24 hrs yet the moon reappears every 24hrs and 49 minutes. Can you explain why this is so?

A solar eclipse happens when the Moon passes between the Sun and the Earth. This casts a shadow over the Earth.

The last solar eclipse over the UK was on 11th August 1999. Solar eclipses do not occur very often.

A lunar eclipse happens when the Earth passes between the Sun and the Moon. This casts a shadow over the Moon.

Lunar eclipses happen in most years.

Eclipses

Where must the Moon be for a solar eclipse to take place?During a solar eclipse the Moon moves directly between the Sun and the Earth.

What happens during a solar eclipse?

During a solar eclipse the Moon blocks the Sun’s rays from reaching part of the Earth.

Where must the Moon be for a lunar eclipse to take place?

During a lunar eclipse the Moon is on the opposite side of the Earth to the Sun.

What happens during a lunar eclipse?

During a lunar eclipse the Earth blocks the Sun’s light from reaching the Moon.

Why are solar eclipses so rare?

- Because the moons orbit is tilted relative to the plane of the Earth’s orbit around the sun the chance of the Sun, Moon and Earth all being perfectly in a line is very rare.

Retrograde Motion21 Apr 2023

WILF: be able to explain how the earth’s rotation causes the apparent motion of the stars and planets.

Starter: Which constellations do you recognise?

Keywords:

Retrograde motion

Constellation

Polaris

21st September

21st June

21st March

21st December

Retrograde Motion:

To see retrograde motion for yourself:

Load Stellarium

Set the date to 23/11/2009

Set the time for 7pm

Search for Mars

Click on one of the nearby stars so the computer keeps that in the centre of the screen.

Move time forward by 1 sidereal week at a time by pressing alt ]

Watch the retrograde motion of Mars

Can you make this happen with any other planets? Why is the effect more pronounced with Mars?

Retrograde Motion:

The planets generally move in one direction across the “fixed” background of stars. Sometimes they appear to slow down and even go in the reverse direction. This is known as retrograde motion.

Background of fixed stars

Where does Mars appear?

1

23

4

5

Measuring the Distance to Stars

21 Apr 2023

WILF: Be able to describe what parallax is and be able to use it to calculate the distance to stars.

Keywords:

Parallax

Parallax angle

What is the parallax angle?

θ

2θ

Original telescope direction

3x1011m

Position of Earth 6 months later

1.5x1011m

The parallax angle (θ) is half of the stars apparent angular motion.

Using trigonometry distances to stars can therefore be calculated.

θ

4000m

2000m

Worked example:

If the object in the diagram had a parallax angle 50. How far away is it?

Sin θ = Opposite/hypotenuse

Sin5 = 2000/d

Therefore d = 2000/sin5

Therefore d = 22947m.

d

Examples using parallax

θ

d

θ

3x1011m

1.5x1011m

Worked example:

If a star had a parallax angle 0.020. How far away is it?

Sin θ = Opposite/hypotenuse

Sin0.02 = 1.5x1011/d

Therefore d = 1.5x1011/sin0.02

Therefore d = 4.297 x 1014m.

How many light years is this?

Light travels at 3x108 m/s.

Therefore light travels

3x108x60x60x24x365

= 9.4608x1015 m/year

Therefore 4.297x1014/ 9.4608x1015

= 0.045 light years.

d

Using Really Small Angles to Measure Distances to Stars

21 Apr 2023

WILF: Be able to use the unit of parsec to calculate distances to stars.

θ

d = 12000m

Keywords:

Parsec

Minute

Second

Arc

Starter: What is the parallax angle for the object in the diagram shown?

3000m

Smaller angles

In a circle there are 3600

We can split each degree of arc up into smaller measurements:

60’ (minutes) of arc = 10

So 100 = 600’ of arc.

Or 0.10 = 6’ of arc.

Because stars are so far away – parallax angles are even smaller than this. Therefore we need a small unit than the minute of arc.

60’’ (seconds) of arc = 1’

So 0.5’ = 30’’ of arc.

So 1 second of arc (1’’) = 1 of a degree3600

Parsec

θ = 1’’

d = 1 parsec

An object whose parallax angle is 1 second of arc is at a distance of 1 parsec.

So an object whose parallax angle is 4 seconds of arc is a distance of 0.25 parsec.

As the angle decreases the distance increases.

Distance in parsec = 1

Angle in seconds

1 parsec is about 3x1013km

Starter: If you look up at the night sky. Is there a way in which you can tell which stars are closest to the Earth?

The Brightest Star 21 Apr 2023

WILF: be able to explain the difference between luminosity and observed brightness and how the colour of a star is related to its temperature.

Keywords:

Luminosity

Observed brightness

Spectrum

Peak frequency

Definitions:

Luminosity – The amount of energy radiated into space every second by a star.

Luminosity depends on:

• The stars temperature (a hot star radiates more energy/second from a given area of its surface)

• The stars size (a bigger star has more surface that radiates energy)

• So a big hot star will be have a higher luminosity than a small cool star.

Observed Brightness – a measure of the light reaching telescope from a star.

This will depend on:

• The distance the star is from the Earth

• The luminosity of a star.

• So just because a star appears bright does not mean it has to be close to the Earth.

http://www.astro.ubc.ca/~scharein/a311/Sim/bbody/BlackBody.html

http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm

Black Body Radiation Applets – Explore how changing the temperature of a star affects the electromagnetic radiation emitted by it.

Star Colours:

All hot objects emit a continuous range of electromagnetic radiation. The surface temperature of a star will determine the wavelength of the electromagnetic radiation we see emitted and hence the colour of the star.

Intensity of radiation at each frequency

wavelengthfrequency

Hotter star

Colder star

The graph shows that:

• a hotter star has a greater area under the graph so the luminosity is greater.

• a hotter star produces a greater proportion of radiation at higher frequencies (it peak frequency is greater).

Cepheid Variable Stars 21 Apr 2023

WILF: Explain what a Cepheid variable star is and how they can be used to measure distances to galaxies.

Keywords:

Cepheid Variable Star

Period

Leavitt

Globular Clusters

Shapley

Curtis

Hubble

Megaparsec

Use the text book pg 218/219 to help you answer the following:

What is a Cepheid Variable Star?

• A Cepheid variable star is a star whose observed brightness varies in a regular pattern.

• What causes the variation in their luminosity?

• It is caused by the star expanding and contracting causing its temperature and hence its luminosity to change.

• What is meant by the period of a Cepheid variable star?

• The time it takes for the star to go from its brightest back to its brightest again.

• What is the relationship between their luminosity and their period?

• The more luminous the star the longer the period is.

• How can this be used to measure the distance to a Cepheid variable star?

• Measure the period of the star and calculate the luminosity based on this.

• Measure the observed brightness of the star

• From the luminosity and the observed brightness the distance to the star can be calculated.

Read the text book pg 220/221.

Complete the following table. In each column outline what theory each astronomer came up with.

Used observations of a Cepheid

variable star in a spiral nebulae to

calculate its distance. Found

out it was about 1 million light years away – far further away than the size of the Milky Way

Felt that the spiral nebulae he had been studying

were very distant from the Milky

Way and were in fact galaxies just like our own Milky

Way.

Thought the Milky Way was at the

centre of the Universe. Said

there were Globular Clusters (clusters of stars) orbiting around our Milky Way

galaxy.

HubbleCurtisShapley

Hubble’s Constant

WILF: be able to calculate the Hubble constant and the distance to distant galaxies given appropriate data.

Keywords:

Speed of recession

Hubble Constant

Megaparsec

Hubble and the Big Bang

Galaxy/object DistanceSpeed of recession

Mpc km/s

S. Mag. Cloud 0.032 170

L. Mag. Cloud 0.034 290

NGC 5457 0.45 200

NGC 4736 0.5 290

NGC 5194 0.5 270

NGC 4449 0.63 200

NGC 4214 0.8 300

NGC 3627 0.9 650

NGC 4826 0.9 150

NGC 5236 0.9 500

NGC 1068 1 920

NGC 5055 1.1 450

NGC 7331 1.1 500

NGC 4258 1.4 500

NGC 4151 1.7 960

NGC 4382 2 500

NGC 4472 2 850

NGC 4486 2 800

NGC 4649 2 1090

The Hubble Constant

• Hubble managed to measure the distance to different galaxies using Cepheid variable stars.

• He also worked out the speed of their recession from “red shift” measurements (how fast they were going away from us).

• Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph.

Speed o

f re

cess

ion (

km/s

)

Distance (Mpc)

Galaxy/object DistanceSpeed of recession

Mpc km/s

S. Mag. Cloud 0.032 170

L. Mag. Cloud 0.034 290

NGC 5457 0.45 200

NGC 4736 0.5 290

NGC 5194 0.5 270

NGC 4449 0.63 200

NGC 4214 0.8 300

NGC 3627 0.9 650

NGC 4826 0.9 150

NGC 5236 0.9 500

NGC 1068 1 920

NGC 5055 1.1 450

NGC 7331 1.1 500

NGC 4258 1.4 500

NGC 4151 1.7 960

NGC 4382 2 500

NGC 4472 2 850

NGC 4486 2 800

NGC 4649 2 1090

The Hubble constant

Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph.

Speed o

f re

cess

ion (

km/s

)Distance (Mpc)

Plot a straight line of best fit on your graph.

Work out the gradient of your line – this is the Hubble constant.

The Hubble constant

Use his data in the table to plot a graph on the axis below – what is the general trend shown by your graph.

Speed o

f re

cess

ion (

km/s

)

Distance (Mpc)

Plot a straight line of best fit on your graph.

Work out the gradient of your line – this is the Hubble constant.

From maths you should know that straight line graphs through the origin are of the form y = mx.

Therefore:

Speed of recession = Hubble constant x distance

From this equation if we know the speed of recession of a galaxy we can work out its distance.

Inside Stars and the Lives of Stars

What is the Sun Made Of? 21 Apr 2023

WILF: Explain how emission and absorption spectra allow us to know what a star is made of.

Keywords:

Emission spectrum

Absorption spectrum

Energy levels

Photon

Electrons in atoms only have certain values of energy. We represent this by drawing them in energy shells.

Sometimes it is easier to draw these energy shells as a “ladder” of energy levels.

1st energy level – lowest energy2nd energy level

All these other possible energy levels exist even though there are no electrons in them

Emission Spectra

When atoms get very hot – electrons are excited from their energy levels to higher energy levels.

The electrons then fall back down to their original energy level and emit a photon of light that is equal in energy to the gap in the energy levels.

This will correspond to a certain colour of light.

Emission Spectra

If excited to different energy levels they will emit different colours of light corresponding to the energy difference.

Absorption Spectra

Stars are blazing balls of gas where many kinds of atoms emit light of all colours.

If you look at the spectrum you should therefore see all colours of the spectrum present.

However as this light travels through the star’s outer atmosphere photons of certain energies will be absorbed by different atoms. These frequencies of light will therefore not appear in the spectrum seen. This is known as an absorption spectrum.

Absorption Spectra

Dark absorption lines appear in the spectrum when an atom absorbs a certain frequency of light causing electrons to jump out to higher energy levels. The frequencies of light not absorbed will be seen.

Which of the mystery elements a, b, c or d are responsible for the absorption spectrum shown.

a b c d

Probing the Atom 21 Apr 2023

WILF: Be able to explain the evidence that revealed the existence of the nucleus in the atom.

Research the following:

What did John Dalton think an atom was?

What was the plum-pudding model of the atom?

What experiment did Geiger and Marsden carry out to show the plum-pudding model was wrong?

How did their experiment show the existence of the nucleus in the centre of the atom?

Good site with information and animation of alpha particle scattering:

http://www-outreach.phy.cam.ac.uk/camphy/nucleus/nucleus1_1.htm

++

++

The Strong Nuclear Force

The nucleus of an atom contains neutrons and protons.

But the protons are all positively charged so they should repel each other.

There is another force present called the strong nuclear force.

It only acts over a very small range and is able to balance out the repulsive electrostatic force.

proton

neutron

Pressure and Volume

WILF: Be able to show and explain how the pressure and volume of a gas are related.

21 Apr 2023

Plot your data on a graph to show how pressure and volume are related.

Now plot a graph of pressure against 1/volume. What do you notice?

Volu

me

pressure

Pre

ssu

re

1/volume

Keywords:Pressure

Kinetic theory

Volume

Conclusion:

When the pressure is increased the volume ___________. The pressure is __________ proportional to the volume.

Pressure is caused when the molecules of a gas collide with the container walls. Each collision causes a tiny force. Together all the forces add up to produce a gas pressure.

When the volume is decreased the pressure __________. This is because……………………..

Pressure and Temperature

WILF: Be able to show and explain how the pressure and temperature of a gas are related.

21 Apr 2023

Keywords:

Kelvin

Absolute zeroTemp/0C

Pressure/kPa

10 9.8

20 10.1

30 10.5

40 10.8

50 11.2

60 11.5

70 11.9

80 12.2

90 12.6

100 12.9

Temp/0CPressure/

kPa

10 9.8

20 10.1

30 10.5

40 10.8

50 11.2

60 11.5

70 11.9

80 12.2

90 12.6

100 12.9

The relationship between temperature and pressure:

Plot the following data on a graph with the axis shown. Extrapolate your graph back to the x axis. What is the temperature where it crosses?

Temperature (0C)0 100-300

Pressure (kPa)

13

Temperature (0C)0 100-300

Pressure (kPa)

13The point where the line crosses the x axis is known as absolute zero. At this temperature the molecules are no longer moving and so there is no gas pressure

The temperature of absolute zero is -2730C

Absolute Zero

The Kelvin Temperature Scale

The Celsius temperature scale was based on the freezing and boiling points of water.

The Kelvin (K) scale starts at absolute zero.

O Kelvin (0 K) is absolute zero (-2730C).

Each graduation on the Kelvin scale is the same as on the Celsius scale

Temperature in 0C = temperature in K – 273.

0 K -2730C

273 K 0 0C

100 0C373 K