· PDF file · 2016-09-02uniform motion in straight line unless ... = average distance between masses = radius if circular orbit describes orbits of 2 bodies about their ... Freshman

www.astro.yale.edu/astro120

Prof. Jeff Kenney Class 2

September 2, 2016

First image of extrasolar planet?

likely image of extrasolar planet

CVSO 30 1200 light years away – planet would be larger than Jupiter VLT telescope Chile Schmidt etal 2016

star

planet

today we know about thousands of exoplanets… …not by imaging, but through other means …. how do we know?

•  scientific idea

•  scientific method

•  scientific theory

Scientific idea (hypothesis)

•  one which can be verified by an experiment (real or imagined)

Scientific idea (hypothesis)

•  one which can be verified by an experiment (real or imagined)

•  one which makes specific predictions that be tested in objective way

scientific method

way to study nature systematically 1.  propose idea

scientific method

way to study nature systematically 1.  propose idea 2.  test idea (this is hard part! objective tests!)

scientific method

way to study nature systematically 1.  propose idea 2.  test idea (this is hard part! objective tests!) 3. accept idea (this is rare!) or reject or revise idea

scientific method

way to study nature systematically 1.  propose idea 2.  test idea (this is hard part! objective tests!) 3. accept idea (this is rare!) or reject or revise idea [return to #1]

Which of the following is a non-scientific idea

A. The earth orbits the sun

B. The sun orbits the earth

C. The moon is made of green cheese

D. The universe is large E. The universe is

expanding

Scientific theory

a body of related hypotheses pieced together to form a self-consistent description of nature

Which  of  the  following  would  cause  a  scientific  theory  to  be  rejected?

A.  It  does  not  agree  with  previous  theories

B.  It  does  not  correctly  predict  experimental  observations

C.  Most  scientists  consider  the  theory  to  be  wrong

D.  The  technology  has  not  yet  been  developed  to  make  the  observations  that  would  test  the  theory  

E.  It  is  not  supported  by  religious  beliefs

Newtonian  mechanics,  which  describes  the  motion  of  objects  when  forces  are  exerted  on  them,  was  accepted  as  a  scientific  theory  that  describes  nature  approximately  

400  years  ago.    It  was  accepted  because  it

A.  was  proposed  by  someone  we  now  know  to  be  a  genius

B.  was  derived  from  fundamental  mathematical  principles

C.  was  handed  down  to  us  by  the  Greeks    

D.  predicted  how  objects  move  under  the  action  of  a  force  

E.  was  supported  by  the  religious  authorities  

theories of motion & gravity Kepler’s law of planetary motion

Newton’s laws of gravity and motion

Einstein’s law of gravity

(good) theories of motion & gravity Kepler’s law of planetary motion Works very well describing a couple of things about orbits in our solar system

Newton’s laws of gravity and motion Works very well describing many things about motion at low speeds and with weak gravitational fields (including outside our solar system) Einstein’s law of gravity Works very well in all known circumstances (including at high speeds and in strong gravitational fields)

(good) theories of motion & gravity Kepler’s law of planetary motion Works very well describing a couple of things about orbits in our solar system

Newton’s laws of gravity and motion Works very well describing many things about motion at low speeds and with weak gravitational fields (including outside our solar system) Einstein’s law of gravity Works very well in all known circumstances (including at high speeds and in strong gravitational fields)

Increasingly general & powerful

Examples of BAD scientific theories

•  geocentric model of solar system •  astrology (or non-scientific idea) •  creationism these have been shown to be wrong

Newton’s First Law of Motion

Body continues in state of rest or uniform motion in straight line unless made to change state by forces acting on it

Newton’s First Law of Motion

Body continues in state of rest or uniform motion in straight line unless made to change state by forces acting on it (i.e., body does not accelerate unless forces act on it)

Newton’s Second Law of Motion Amount of acceleration a that a force F can produce depends directly on mass m of object being accelerated

F=ma

Newton’s Second Law of Motion Amount of acceleration a that a force F can produce depends directly on mass m of object being accelerated F=ma

Fb = Ft

mbab = mtat

mb > mt

à ab < at tennis ball receives larger acceleration if same force applied to both since it has smaller mass

basketball mb

tennis ball mt

Newton’s Third Law of Motion

When 2 bodies interact, they create equal and opposite forces on each other

Newton’s Third Law of Motion

can call this force Fbt (force on b due to t) or Fb (force on b)

Fb Ft

When 2 bodies interact, they create equal and opposite forces on each other

can call this force Ftb (force on t due to b) or Ft (force on t)

Fb = mbab (N2) Ft = mtat (N2)

Ft = Fb (N3) mtat = mbab

at = (mb/mt) ab

mb

if mb = 10 mt then at = 10 ab

Fb Ft

ab at

mt

If you’re standing in a train moving on level ground at a constant velocity of

200mph and leap straight up A.  You will land in the same place B.  You will land slightly behind

your starting point C.  You will land far behind your

starting point D.  You will land slightly in front of

your starting point E.  Where you land depends on

whether the train is moving forwards or backwards

Newton’s Law of Gravity Every mass exerts a force of attraction on every other mass

F = force m1 = mass of body 1 m2 = mass of body 2 R = distance between m1 and m2

G = 6.67x10-11 Nt m2 kg-2 Gravitational constant

Newton’s Form of Kepler’s 3rd Law follows directly from Newton’s Laws of motion and gravity

M1 = mass of body 1 M2 = mass of body 2 P = orbital period (time) a = semi-major axis of elliptical orbit (distance) = average distance between masses = radius if circular orbit

describes orbits of 2 bodies about their center of mass

Newton’s Form of Kepler’s 3rd Law follows directly from Newton’s Laws of motion and gravity derivation on class website…

M1 = mass of body 1 M2 = mass of body 2 P = orbital period (time) a = semi-major axis of elliptical orbit (distance) = average distance between masses = radius if circular orbit NOTE!! THIS “a” IS DIFFERENT FROM “a” FOR ACCELERATION!! sorry…

describes orbits of 2 bodies about their center of mass

Newton’s Form of Kepler’s 3rd

Law

for special case of planets in our solar system: M1 = 1 Msun = 2x1033 gm M2 = Mplanet << 1 Msun e.g. Mearth = 6x1027 gm if M2 << M1 then (M1+M2) ≈ M1 = 1 Msun

à P2 ≈ a3 iff P in years, a in AU Kepler’s 3rd Law of Planetary Motion

in many cases this assumption OK but NOT for one of the HW problems!!

Kepler’s 3rd Law of Planetary Motion P2 ≈ a3

Star and planet both orbit around center of mass

Planet and star orbiting center of mass

Center of mass can be inside one of the bodies!

Planet and star orbiting center of mass

Doppler shifts from orbiting star

Wavelength of light shifted by motion

An earth-sized extrasolar planet orbits 1 AU from a star of 1 solar mass. What is the

approx period of the star’s wobble?

A.  4 yrs B.  0.25 yr C. 1 yr D. 0.5 yr E. Not enough information

given

An earth-sized extrasolar planet orbits 1 AU from a star of 4 solar masses. What is the

approx period of the star’s wobble?

A.  4 yrs B.  0.25 yr C. 1 yr D. 0.5 yr E.  just hurry up and finish

class!

Astronomy 120 Lec 1-5: intro, physics review Lec 6-8: stars Lec 9-14: galaxies, clusters & dark matter Lec 15-18: active galaxies & black holes Lec 19-25: cosmology & the universe For full syllabus see website www.astro.yale.edu/astro120

Remote polling & peer instruction •  More discussion & learning in class àAttendance important! àClicker responses will be used to track attendance!

(starting 3rd week) •  Less material covered in class àImportant to read textbook before class! àOn-line Reading quizzes Must complete by 9am the day of the class! -> Starts next week (for class 3), but will start to

count 3rd week (for class 4) Accessed from Canvas, “reading quiz”

Clicker distribution •  Everyone gets their own registered

clickers for the semester

•  Need only one clicker for all Yale clicker classes (don’t need one for each class)

•  Sign them out of Bass Library (but you

may want to wait until you are sure you are taking the class)

•  then register clicker on canvas

textbook

•  Universe (Freedman, Geller, Kaufmann) 10th edition

•  E-book recommended (LaunchPad) •  website has link •  “hardcopies” (used, looseleaf) at Yale

bookstore or through Amazon (10th or 9th or 8th editions are OK)

Homeworks

•  ~weekly •  Due on Wednesdays •  1st HW due in 1.5 weeks, Wed Sept 14

Discussion Sections

•  Optional but strongly encouraged •  Goals: help with homework assignments & class

concepts •  Starts end of next (2nd) week •  possible section times (3 or 4 sections total?): Fri 11:35am Mon 8pm Tues 4pm, 7pm

Grading 25% Midterm exam 30% Final exam 25% Weekly Homework 8% Reading quizzes 5% Attendance 5% Observing & Planetarium assignment 2% QR Assessments

Please take QR Assessment! See Canvas, ASTR 120 01 (F16) Quizzes “Astro QR I Fall 2016 (start of semester)”

Class website

main site: www.astro.yale.edu/astro120

but some things on canvas

Introductory Astro courses this semester (FALL 2016) all count for Sc; no Yale prereqs

Astro 030 Search for Extraterrestrial Life (Faison) TT 4:00 not QR; Freshman seminar Astro 105 Earth in the Cosmic Context (Laughlin) TT 1:00 not QR; not intended for Science majors Astro 120 Galaxies & the Universe (Kenney) MW 1:00 QR; not intended for Science majors Astro 130 Origins & Search for Life in the Universe (Fischer) MWF 10:30 not QR; not intended for Science majors Astro 155 Introduction to Astronomical Observing (Faison) M 7:00 ½ credit lab, not QR, OK for Science majors, counts for Astro major Astro 255 Research Methods in Astrophysics (Geha) MWF 3:30 QR, OK for Science majors, counts for Astro major