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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 2r v T 2r 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 2016 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 Nkg1 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 Animated Science 2016 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 Animated Science 2016 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 2016 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 2016 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. 2r 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 2016 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 2r 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 = 2r/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 2016 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) 2r 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 2016 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 2016 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 Animated Science 2016 Answers after this slide.... Animated Science 2016 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 2016 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 2r 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 2016 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 2016 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 Animated Science 2016 Something new I learned today...... Something new I learned today...... Something new I learned today...... Something I still need help with...... Something I still need help with...... Something I still need help with...... Something new I learned today...... Something new I learned today...... Something new I learned today...... Something I still need help with...... Something I still need help with...... Something I still need help with...... Something new I learned today...... Something new I learned today...... Something new I learned today...... Something I still need help with...... Something I still need help with...... Something I still need help with......