### A Sense of Scale

```A Sense of Scale: How fast?
The International Space Station
orbits the Earth several times a day.
Information:
• The ISS spot the station page will tell you when you
are able to see the station in your hometown.
• The average diameter of the Earth is 12742 km.
• The ISS orbits at a height of 370km.
How many times does it orbit the Earth each day?
How fast does the ISS travel?
A Sense of Scale: How big?
Our Solar system is big, at 4.50 x 108 km from the sun
to Neptune, but how does this compare to other
distances?
A light year (ly) is the distance light travels (in vacuum)
in a year. 1 ly is 9.46 x 1012 km
Our galaxy, the Milky Way, is estimated to be
110 000 ly in diameter.
How many times bigger is this than our solar system?
A Sense of Scale: Our Solar System
Our Solar System consists of the sun
and 8 planets which orbit it.
It is often represented in diagrams
(such as the one on the next slide) to convey a sense
of how large or small Earth is compared to the other
planets and the sun. But, how representative is this?
Do we get a proper ‘sense of scale’ from it?
This activity will help you appreciate the true scale of
our Solar System.
A Sense of Scale: Our Solar System
The diameter of a tennis ball is 6.7cm.
Using this to represent the Earth, work out
the size of the sun and the other planets
in the Solar System.
Can you think of a spherical
object which could be used to represent each one?
A Sense of Scale: Our Solar System
If the ‘scaled sun’ was in this room, where would the
planets be?
A Sense of Scale: Our Solar System
Choose something large, such as a long corridor, the
school hall, a football pitch, netball court or a 100m
running track. Measure it (if necessary).
If the sun were at one end and Neptune at the other,
where would the other planets be?
How big would:
– The Earth be?
– The sun be?
Teacher notes: A Sense of Scale
Through these activities, pupils will gain a sense of the size and distances that exist
within our solar system.
There are two short ‘starter’ activities: ‘How fast?’ and ‘How big?’ and one longer activity
‘Our Solar System’, which could be split into three shorter activities. The tasks are aimed
at Years 9 to 11.
It is suggested that pupils approach the longer task as a problem solving activity, working
in pairs or threes.
Teacher notes: How fast?
This is a short problem that pupils should find engaging, particularly if the spotter is used
live.
Use the ISS spotter to find two consecutive times that the ISS is overhead.
If the sighting opportunity is from 05:06 to 05:10, the sighting could be assumed to be at
05:08.
The ISS actually takes 91 minutes to orbit the Earth, but the time from one visible pass to
the next can be a little longer at 95 or 96 minutes.
Calculations:
Orbits each day = 24 x 60 ÷ 91 = 15.8 orbits (will be 15 orbits if 96 minutes is used)
Distance it orbits = π x (1270 + 370 + 370) = 6315km
Speed
=
6315
1.52
= 4154 kmh-1
Time = 91÷60 = 1.52 hours
Can compare this with max speed recorded
for an F1 car of 370 kmh-1
Teacher notes: How big?
This is a short problem for pupils to utilise their index notation skills.
Calculation:
Size of the Milky Way = 110 000 x 9.46 x 1012
Size of the Milky Way = 1.1 x 105 x 9.46 x 1012
or
1040600 x 1012
Size of the Milky Way = 10.406 x 1017 = 1.04 x 1018
How many times bigger than our solar system = (1.04 x 1018 ) ÷ (4.50 x 108 )
How many times bigger than our solar system = (1.04 ÷ 4.50) x (1018 ÷ 108 )
How many times bigger than our solar system = 0.2311 x 1010 = 2.31 x 109
Teacher notes: Our Solar System
Both a structured and an unstructured format are provided.
• For increased challenge for pupils, simply give them ‘Our Solar System Data sheet’
and let them devise their own ways of calculating and recording.
• Pupils requiring some scaffolding should be given page 1 of ‘Our Solar System’ and
then page 2 once they have completed activity 1.
• Slides 4 to 6 can be used to set the initial problem and the information for planet
sizes handed out.
• The second and third parts of the problem – finding the relative distances (slide 7)
and thinking about a scale model (slide 8) – could be used as extension activities or
as a whole class continuation of the problem.
If a few pupils are stuck, using a whole class mini-plenary to discuss approaches to
solving the problem may be helpful.
If many pupils are stuck, using an example of how to find real distances from a map may
help.
Teacher notes: Our Solar System
Planet sizes
This activity may seem challenging to begin with, but to determine the size of the planets,
pupils simply need to use ratio (although this may be problematic in itself).
Example:
Scaled size of Earth: Actual size of Earth
must be in the same ratio as
Scaled size of sun: Actual size of sun
Scaled size of sun
Actual size of sun
Scaled size of Earth
=
Actual size of Earth
so
Scaled size of Earth
Scaled size of sun
=
Actual size of sun
x
Actual size of Earth
Teacher notes: Our Solar System
Object
Diameter
(km)
Scaled
diameter
(cm)
Possible object to approximately represent it
Sun
1 392 000
731.6
Tricky! As a sense of size, the width/length of a
classroom (as appropriate) or mobile planetarium
(hemisphere) eg here – seats 60 adults.
Mercury
4 879
2.6
Walnut
Venus
12 104
6.4
Tennis ball (6.7cm)
Earth
12 742
6.7
Tennis ball (6.7cm)
Mars
6 780
3.6
Ping Pong ball (3.8-4cm)
Jupiter
139 822
73.5
Fitness ball (usually 55, 65 & 75cm)
Saturn
116 464
61.2
Fitness ball (usually 55, 65 & 75cm)
Uranus
50 724
26.7
Small beach ball (30cm)
Neptune
49 244
25.9
Size 5 Football or netball (22cm)
Having some of these objects available will help students to appreciate the sizes involved.
Teacher notes: Our Solar System
Planet distances
The calculations for this activity are similar to those used in the planet sizes. To maintain
comparisons with using the tennis ball as the Earth, the same scalar should be used.
Example:
Scaled size of Earth: Actual size of Earth
must be in the same ratio as
Scaled distance to the sun: Actual distance to the sun
Scaled distance to the sun
Actual distance to the sun
Scaled size of Earth
=
Actual size of Earth
so
Scaled distance to
the sun
=
Actual distance to
the sun
Scaled size of Earth
x
Actual size of Earth
Teacher notes: Our Solar System
Planet distances
Part of this activity is unique to the school location, so may need a little preparation.
To bring the distances to life, it would be helpful to have a local map to hand to gain a
better sense of where the planets are – for Earth and perhaps Neptune, if no others.
It might be engaging for (some) pupils to identify which of the planets would be closest to
their home.
Alternatively, using an online map which can be re-scaled is helpful; Google Earth, or
similar, has a measuring tool that could be used to locate a place which is the right
distance away from the school.
Teacher notes: Our Solar System
Object
Sun
Distance from sun Scaled
(km)
distance
0
0
Mercury
57000000
300m
Venus
108000000
568m
Earth
150000000
788m
Mars
228000000
1.2km
Jupiter
779000000
4.1km
Saturn
1430000000
7.5km
Uranus
2880000000
15.1km
Neptune
4500000000
23.7km
Likely place
In the room
Other end of (a large) school or out
on the school field
Teacher notes: Our Solar System
Scale model
The calculations are similar but values will depend on the ‘venue’ chosen.
Actual distance from sun to planet
Scaled distance from
sun to planet
=
x
Actual distance from sun to Neptune
Scaled distance from
sun to Neptune
For the relative planet sizes, the following should be used:
Scaled diameter
of planet
Actual diameter of planet
=
Actual distance from sun to Neptune
x
Scaled distance from sun to
Neptune
The answers on the next page are based on using a 100m running track. Markers (metre
rules stuck in the ground or pupils holding them) could be placed at the correct locations
– perhaps with very small items such as a grain of rice or a small sequin to represent
smaller planets, perhaps a pea to represent Jupiter. The sun would be the size of a
walnut.
Teacher notes: Our Solar System
Object
Sun
Distance from sun (km)
0
Mercury
57000000
Venus
108000000
Earth
150000000
Mars
228000000
Jupiter
779000000
Saturn
1430000000
Uranus
2880000000
Neptune
4500000000
Scaled distance (m) Scaled size (mm)
0
30.9
1.27
0.11
2.40
0.27
3.33
0.28
5.07
0.15
17.31
3.11
31.78
2.59
64.00
1.13
100m
1.09
Acknowledgements
Solar system image: original copyright NASA, accessed http://nineplanets.org/ 2/1/14
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