Transcript iGCSE Forces and Astronomy 1d

Section 1d: Forces and Motion... “Astronomy”
1.32 Understand gravitational field strength, g, and recall that it is
different on other planets and the moon from that on the Earth
1.33 Explain that gravitational force:
•
causes moons to orbit planets
•
causes the planets to orbit the sun
•
causes artificial satellites to orbit the Earth
•
causes comets to orbit the sun
1.34 Describe the differences in the orbits of comets, moons and
planets
1.35 Use the relationship between orbital speed, orbital radius and
time period
v
2r
v
T
2r
T
Scan me for
Additional Resources
1.36 Understand that:
•
the universe is a large collection of billions of galaxies
•
a galaxy is a large collection of billions of stars
•
our solar system is in the Milky Way galaxy.
NB: When you work through this booklet, try the iSpring
Quiz online to check your learning as you go
mv2
F
r
g
GM
r2
T2 
4 3
r
Gm
Animated Science
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1.32 Understanding gravitational field strength, g
GCSE Gravitational Field Strength “g” is
defined as a region in space where a small
test mass feels a force due to its mass. We
can define it two ways, but both are
equivalents (the same). The example is for a
baby with a mass of 10kg on Earth
F = ma
w = mg
F
a
m
Force = mass x acceleration
Weight = mass x gravity
100 N
g
 10 Nkg1
10kg
or
W
g
m
To understand this better in A-Level
Physics we can more usefully define “g”
in terms of the mass of the planet and its
radius, with the universal gravitational
constant “G”. The example below is
shown for the earth
g
g
6.67408 × 10-11 m 3 kg -1 s -2  5.972 × 10 24 kg
6371×10 m
3
6.67408 × 10-11  5.972 × 10 24
B/C
6371×10 
3 2
g  9.8196ms -2
g  9.81ms -2
g  9.81Nkg 1
In your exam you can
use...
g = 10ms-2
g = 10Nkg-1
2
GM
g 2
r
A*/A
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1.32 Recall that “g” is different on other planets and the moon from that on the
Earth
Challenge Task: Use the ABasic Task: Use information online to fill in all the
blanks in the table for the missing planets then
discuss with a partner
Item
Mass / kg
3.3x1023
4.87x1024
Earth
5.976x1024
Mars
6.42x1023
1.90x1027
Saturn
5.69x1026
Uranus
8.68x1025
1.03x1026
Pluto ( Dwarf) 1.46x1022
Moon
7.35 × 1022
Mercury
Mass /kg
3.30E+23
5.98E+24
6.42E+23
8.68E+25
1.46E+22
7.35E+22
http://hyperphysics.phyastr.gsu.edu/hbase/solar/soldata2.html
B/C
Diameter/km
(Equatorial)
4878
12104
12756
6794
142,984
120,536
51,118
49,528
2370
3474
Level formula to calculate
“g”
A/A*
Radius/km
Radius/m
G
g / ms-2
2439
2,439,000
6.67E-11
3.70
6378
3397
6,378,000
3,397,000
6.67E-11
6.67E-11
9.80
3.71
25559
25,559,000 6.67E-11
8.87
1185
1737
http://www.universetoday.com/35
565/gravity-on-other-planets/
1185,000
1737,000
6.67E-11
6.67E-11
0.69
1.62
https://en.wikipedia.org/wiki/Categor
y:Solar_System
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1.33 Explain that gravitational force causes...
moons to orbit planets
causes the planets to orbit the sun
causes artificial satellites to orbit the Earth
causes comets to orbit the sun
1.
When we think about “g” acting on objects, it is almost like a
plane flying on a string around a spike in the ground.
2.
The plane is pulled towards the centre of the spike constantly
The forwards motion ensures it does not crash into the spike.
3.
The centripetal forces caused by the gravitational field make
moons, planets, satellites or comets to orbit in a circular or
elliptical fashion.
4.
The forwards velocity of a planet ensures it does not crash
into the sun
It helps to use the A-Level formula to
explain this (can use words instead)
Centripetal force is increased when:
•
•
•
the linear speed is increased;
the mass is increased;
the radius is decreased
v
F
mv
F
r
2
Animated Science
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1.34 Describe the differences in the orbits of comets,
moons and planets
Planets
The planets take different amounts of
time to go around the Sun. A single
orbit is called the planet's year, and
the further out a planet is the longer its
year takes.
The orbits of the planets in the solar
system are almost circular with the Sun
near the centre. Many diagrams show
the orbits very squashed from top to
bottom.
Asteroids
Asteroids are rocky objects, smaller
than planets. Most of them are found
in an 'asteroid belt', in orbit around the
Sun between Mars and Jupiter. The
minor planet Ceres is found here, too.
Comets
Comets are balls of ice and dust in
orbit around the Sun. The orbits of
comets are different from those of
planets - they are highly elliptical. A
comet's orbit takes it very close to the
Sun speeding up and then far away
again. The time to complete an orbit
varies - some comets take a few years,
while others take millions of years to
complete an orbit.
Asteroids can crash into each other.
When they do, they may break apart
and their orbit may change.
Satellites
These can be either manmade in terms
of weather, telescopes, TV, GPS or spy
satellites or natural such as our own
moon and placed in fixed orbit.
Dwarf Planet
A dwarf planet is a planetary-mass
object that is neither a planet nor
a natural satellite. It is in direct orbit
of the Sun, and is massive enough for
its gravity form a sphere but has not
cleared the neighbourhood of other
material around its orbit (i.e. Rocks)
as “g” gravity caused by the planet is
quite low.
Animated Science
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1.35 Use the relationship between orbital speed, orbital radius and time period
For GCSE Physics we say that each solar
body will follow an orbit in a time
according to a simple formula which
relates radius of orbit, and velocity of
body.
2r
T
v
From this equation we can see that the a
larger orbit will mean a longer time
period. This means that the velocity of
orbit will be lower for planets further
away. (see graph for examples).
This is a simple version of a more complex
(more accurate equation) and works pretty
well for the moon but as you get further
away it is not so good.
Animated Science
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1.35 Use the relationship between orbital speed, orbital radius and time period
Worked Example..... Earth
Radius of orbit = 149.6 million km
Time for Orbit = 365.25 days
2r
T
v
r= 149.6 x 106km
r = 149.6 x 109m
r = 1.496 x 1011m
T = 365.25 * 24 * 60 * 60
T = 31557600s
v = 2r/T
v = (2 * 1.496 x 1011m) / 31557600s
v = 29,785.67ms-1
v = 29,785 ms-1
v= 29,790 ms-1 (4 sig figs)
v= 29,800 ms-1 (3 sig figs)
Animated Science
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1.35 Use the relationship between orbital speed, orbital radius and time period
Basic Task: Use information online to fill in all the blanks in
the table for the missing planets then compare the orbital B/C
velocities to the previous graph to check if they are correct.
Body
Distance from
Sun (106 km)
Distance
/m
57.9
108.2
149.6
227.9
778.6
1433.5
2872.5
4495.1
5906.4
57900000000
1.082E+11
1.496E+11
5.9064E+12
Orbital
Period
(days)
88
224.7
365.2
687
4331
10747
30589
59800
90560
0.384
384000000
27.3
Mercury
Venus
Earth
Jupiter
Uranus
Pluto
MOON
(to Earth)
2r
T
v
7.786E+11
2.8725E+12
Challenge Task: Use the formulae to
calculate the orbital velocities then
compare to the previous graph.
Orbital
Orbital Period
Velocity
/s
(m/s)
7603200
47848
19414080
35018
31553280
29790
A*/A
Orbital
Velocity
(km/s)
47.85
35.00
29.80
374198400
13074
13.10
2642889600
6829
6.80
7824384000
4743
4.70
2358720
1023
1.00
NB: remember to convert to metres
and seconds before you calculate
the orbital velocity
Animated Science
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1.36 Understand That: the universe is a large collection of billions of galaxies, a
galaxy is a large collection of billions of stars, our solar system is in the Milky Way
galaxy
Our local area of space is not just the
planets but is part of a vast disc of
matter including other stars and
black holes spinning like a vast
catherine wheel.
When we look out we might see stars
in another arm or those in other
galaxies, far, far away where we have
no idea what is taking place....
Animated Science
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1.35 Use the relationship between orbital speed, orbital radius and time period
Kepler studied planetary bodies and realised that planets
don’t actually orbit in a circle but actually speed up and
slow down as the move in an ellipse.
This means our Maths is adjusted so that the area swept
out by the motion of the body is always the same each
second, so that when the body is further away it reduces
speed His formula for A-Level Physics was...
4 3
T 
r
Gm
T 2  r3
In essence this showed that the further you are away the
longer the orbit time is.
We could plot a graph in terms of “astronomical units”
(mean distance from Earth->Sun) against the time for
orbit in Earth years. We get an amazing graph!
r3 / astro units
2
T2 / earth years
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Answers after this
slide....
Animated Science
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1.32 Recall that “g” is different on other planets and the moon from that on the
Earth - Answers
Item
Mass / kg
Mass /kg
Diameter/km
(Equatorial)
Radius/km
Radius/m
G
g / ms-2
Mercury
3.3x1023
3.30E+23
4878
2439
2439000
6.67E-11
3.70
Venus
4.87x1024
4.87E+24
12104
6052
6052000
6.67E-11
8.87
Earth
5.976x1024
5.98E+24
12756
6378
6378000
6.67E-11
9.80
Mars
6.42x1023
6.42E+23
6794
3397
3397000
6.67E-11
3.71
Jupiter
1.90x1027
1.90E+27
142,984
71492
71492000
6.67E-11
24.81
Saturn
5.69x1026
5.69E+26
120,536
60268
60268000
6.67E-11
10.46
Uranus
8.68x1025
8.68E+25
51,118
25559
25559000
6.67E-11
8.87
Neptune
1.03x1026
1.03E+26
49,528
24764
24764000
6.67E-11
11.21
Pluto ( Dwarf)
1.46x1022
1.46E+22
2370
1185
1185000
6.67E-11
0.69
7.35 × 1022 7.35E+22
3474
1737
1737,000
6.67E-11
1.62
Moon
Animated Science
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1.35 Use the relationship between orbital speed, orbital radius and time period –
Answers
Body
Distance from
Sun (106 km)
Distance
/m
Mercury
57.9
57900000000
Orbital
Period
(days)
88
Venus
108.2
1.082E+11
224.7
19414080
35018
35.00
Earth
149.6
1.496E+11
365.2
31553280
29790
29.80
Mars
227.9
2.279E+11
687
59356800
24124
24.10
Jupiter
778.6
7.786E+11
4331
374198400
13074
13.10
Saturn
1433.5
1.4335E+12
10747
928540800
9700
9.70
Uranus
2872.5
2.8725E+12
30589
2642889600
6829
6.80
Neptune
4495.1
4.4951E+12
59800
5166720000
5466
5.40
Pluto
MOON
(to Earth)
5906.4
5.9064E+12
90560
7824384000
4743
4.70
0.384
384000000
27.3
2358720
1023
1.00
2r
T
v
Orbital
Orbital Period
Velocity
/s
(m/s)
7603200
47848
Orbital
Velocity
(km/s)
47.85
NB: remember to convert to metres
and seconds before you calculate
the orbital velocity
Animated Science
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Lesson Plan 1 – 30 mins (can be expanded)
Timing
Task
Assessment
Introduction to the Unit of work and pupils form into
pairs and log onto a computer or use tablet PC, pupils
4mins
Starter... Load iSpring Quiz – Question 1 – sorting planets into order
All pupils require a printed booklet (A5 size) as record
of work and for revision later.
4mins
10mins
Teacher explanation of “g” using basic and advanced
formulae Slide 2
Pupils research and fill in Table 1 on slide 3 – “g” for
planets of Solar System. OR for challenge they can use
A-Level formulae (require science calculators /
download Excel information or use QR readers to look
on internet). Note this is an extension to calculate.
NB: Print a version of the results so they can check
4mins
Slide 4 – Teacher explanation of centripetal forces on
solar system bodies – analogy plane on spike. Pupils
can use the basic ideas OR A-level formulae to frame
their understanding
5mins
Pupils read information slides 4 and 5
iSpring – Q3 – sorting “g” for different planets using calculations or
their tables.
Then try Q4 or Q6 on filling in word bank on “g”.
Some students may also like to watch a 5 mins YouTube Video to
recap either basic version of “g” OR advanced version from A-Level
Q7 – is a duplicate of calculation already completed in table
Tackle questions from quiz 8-12 on circular motion and planets
Exit Tickets/ Review - Something new I learned today......
3mins
& Something I still need help with......
30mins
Animated Science
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Lesson Plan 2 – 30 mins (can be expanded)
Timing
Task
5mins
Recap from last lesson – pupils use a whiteboard to
show what they know from the last session
5mins
Slide 6 – discuss with pupils idea behind the formulae
and maths behind it.
Slide 8 – pupils either fill in from internet OR calculate
formula. You may give a more simple version for lower
ability students. NB: they should all calculate
something for exam and may find the units tricky to
manage.
15mins
NB: Print a version of the results so they can check
Assessment
Question 13 – calculation & Can watch quick 3mins video if stuff
Question 14 – Keplers – but they might guess it in any event!
Slide 9 – pupils can read and you may give input in
ideas, if unsure of pictures.
Slide 10 – explain kepler’s law to any interested
students who are looking at A-level Physics you will
need to point out the axis configuration on the graphs.
5mins
Check quiz scores for pupils, they can then revisit
questions to improve Score.
30mins
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