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Key Stage 5 – estimator

Notes for teachers

At a glance

This activity introduces higher attaining students to the study of . They apply ideas about Doppler shift in learning about their detection, and ideas about momentum in estimating their . Students finish by comparing two exoplanets to in our own . Might the exoplanets harbour extraterrestrial life?

The activity is best incorporated when teaching about astrophysics, cosmology or the structure of the Universe. It can be tackled in class or as homework.

Learning Outcomes

 Students apply ideas about Doppler shift.  Students employ ideas about the conservation of momentum to estimate the mass of an exoplanet.  Students interpret and compare data about planets within and outside the Solar System.

Each pair of students will need

 1 copy of the three pages of the pupil worksheet  Access to the Internet www.oxfordsparks.net/planet

Possible Lesson Activities

1. Starter activity  Show the animation ‘Rogue ’ to the class.  Repeat the viewing, focusing on the section on exoplanets from 1:32 to 2:16.  Ask students to suggest how exoplanets might be discovered, given their great distance from Earth and the fact that they cannot be observed directly with the or an ordinary .

2. Main activity  Students read the information on the first page of the pupil worksheet. This page outlines three methods of exoplanet detection, and explains one – the Doppler method – in greater detail. Check that students understand what they have read, and allow time for discussion. Show the animation at www.eso.org/public/unitedkingdom/videos/eso1035g/ to further elucidate the Doppler method for finding exoplanets.  Students work through steps 1 to 5 on the sheets b. Emphasise throughout that they are estimating values rather than calculating them precisely. Please see the following pages for answers to each step.  Student pairs discuss the points in step 6. The exoplanet is not habitable since its temperature is so high owing to its close proximity to its .  Students apply their learning to a second exoplanet, 55 Cancri d, which one of a pair of , 55 Cancri A. The following pages give answers to parts a to d.  Student pairs discuss part e in the section on 55 Cancri d.

3. Plenary  Lead a discussion on exoplanets. How likely is it that some support life? Is the research expenditure justified?  Suggest that students explore PlanetHunters.org at home. Maybe they will discover their own exoplanet.

Web links

Web link 1: www.eso.org/public/archives/presskits/pdf/presskit_0005.pdf Useful background information about exoplanets

Web link 2: www.planethunters.org Citizen science project in which volunteers analyse data to search for exoplanets.

Web link 3: www.astronomynotes.com/solfluf/s12.htm Further details about finding exoplanets

Web link 4: http://eo.ucar.edu/staff/dward/sao/exoplanets/methods.htm Further details about finding exoplanets including an animation www.oxfordsparks.net/planet

Web link 5: www.kcvs.ca/martin/astro/au/unit7/164/chp16_4.html Students can simulate the motion of exoplanets on this web site.

Web link 6: http://home.strw.leidenuniv.nl/~keller/Teaching/ADA_2011/ADA_2011_L06_Exoplanets.pdf Teacher background information.

Web link 7: http://spacemath.gsfc.nasa.gov/ This site from NASA has a huge number of engaging maths problems linked to astrophysics, cosmology and the Universe.

Answers to calculation questions

Step 1

a Rearranging ≈ gives

v ≈ × c

Substituting values into the rearranged equation gives v ≈ [(656.300123 nm – 656.300000 nm) / 656.300000 nm] × (3 × 108 m/s) v ≈ 56.2 m/s b The graph shows a similar maximum to that calculated above.

Step 2 The graph shows that the is approximately 4 days.

Step 3

Rearranging / = 4 / G gives

2 r = [(T G )/ 4 ]

The values to substitute are: T = 4 days = 4 × 24 × 60 × 60 seconds = 346 × 103 seconds

G = 6.67 × 10-11 m3 kg-1 s-2

30 = 2.20 × 10 kg r = [(346 × 103 s × 346 × 103 s × 6.67 × 10-11 m3 kg-1 s-2 × 2.20 × 1030 kg) / 4 ] r = 12 × 109 m

www.oxfordsparks.net/planet

Step 4 speed = distance = 2πr = 2π × 12 × 109 m

So speed = 2π × 12 × 109 m / 345,600 s = 220 × 103 m/s

Step 5

Rearranging = gives

= /

= (2.2 × 1030 kg × 56.2 m/s) / 220 × 103 m/s

= 560 × 1024 kg

In this step the assumption has been made that it is appropriate to use a value of maximum radial velocity for the star, and the orbital speed of the planet.

55 Cancri d a Orbital period ≈ 14 = 14 × 365 × 24 × 60 × 60 seconds = 440 × 106 seconds b

/ = 4 / G 2 so r = [(T G )/ 4 ]

r = [(440 × 106 s × 440 × 106 s × 6.674 × 10-11 m3 kg-1 s-2 × 1.89× 1030 kg) / 4 ] r = 2.9 × 1012 m c For 55 Cancri d:

distance = 2πr = 2π × 2.9 × 1012 m = 18 × 1012 m

speed =

= 18 × 1012 m / 440 × 106 s = 41 × 103 m/s

www.oxfordsparks.net/planet

For Earth:

distance = 2πr = 2π × 150 × 106 × 103 m = 940 × 109 m

speed =

= 9.4 × 1011 m / (365 × 24 ×60 × 60) s = 30 × 103 m/s The speeds of the two planets are similar, with 55 Cancri d moving at a slightly greater speed. d The mass of 55 Cancri d is approximately three times greater than that of the planet with the greatest mass in the table, . Its orbital period is approximately (14 × 365) = 5110 days, which is slightly greater than that of Jupiter. The distance of 55 Cancri d from its star is much greater than the distance of any of the other planets in the table from their stars.

www.oxfordsparks.net/planet