Week 4: Light / Solar System HW 2 past due (any submission before - - PowerPoint PPT Presentation

▶
week 4 light solar system
SMART_READER_LITE
LIVE PREVIEW

Week 4: Light / Solar System HW 2 past due (any submission before - - PowerPoint PPT Presentation

Mar 22, 2024 292 likes •512 views

Week 4: Light / Solar System HW 2 past due (any submission before now is OK) HW 3 due on Thursday @ 10:45am Read Ch. 5 (except 5.5), and 7.1, 8.1-2, 11.1-2 for Thursday ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 1 JCMT ALMA

slide-1
SLIDE 1

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Week 4: Light / Solar System

1

HW 2 past due (any submission before now is OK) HW 3 due on Thursday @ 10:45am Read Ch. 5 (except 5.5), and 7.1, 8.1-2, 11.1-2 for Thursday

slide-2
SLIDE 2

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 2

Life on Mars VENUS?!?!?!

JCMT ALMA

slide-3
SLIDE 3

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 3

“blueshifted” “redshifted” unshifted unshifted

z = ∆λ λ = ∆ν ν

<latexit sha1_base64="STxWXR7tpGVxIUjG4Vm4zWTgYDw=">ACJHicbVBNS8MwGE7n15xfVQ8iXoJD8DTaeXAgwlAPHie4D1jLSN0C0vTkqTCLPsxXvwrXjxMxYMe9OrPMPsQdPOFhIfng+R9vJhRqSzrzcjMzS8sLmWXcyura+sb5uZWTUaJwKSKIxaJhockYZSTqKkUYsCAo9Rupe93yo12+IkDTi16oXEzdEbU4DipHSVMs8uYWn0AkEwqlzQZhC0GE67aN+gNmDzRor5aZt4qWKOBs8CegHy59DnYef/arbTMZ8ePcBISrjBDUjZtK1ZuioSimJF+zkiRHuojZpashRSKSbjpbswPN+DCIhD5cwRH7O5GiUMpe6GlniFRHTmtD8j+tmaig5KaUx4kiHI8fChIGVQSHjUGfCoIV62mAsKD6rxB3kC5E6V5zugR7euVZUCsW7KNC8Uq3cQbGkwV7YB8cAhscgzK4BVQBRjcgQcwAE/GvfFovBivY2vGmGS2wZ8xPr4BaiCpGg=</latexit>

Allows us to infer motions along the “line of sight”

Doppler Shift

slide-4
SLIDE 4

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

4

i.e., the difference b/t energy levels is NOT exact

Motion-induced Broadening (small Doppler shifts cause lines to appear more broad) Other Types of Broadening

  • Thermal Broadening
  • Rotational Broadening
  • Turbulent Broadening
  • Natural Broadening
  • Pressure Broadening
  • Zeeman Broadening

broadened

slide-5
SLIDE 5

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Natural Broadening

5

dNphot dt = n2A21

<latexit sha1_base64="dhIj1pfrbqTDAnhLXGRNS3H5zk=">ACEXicZVA9SwNBEN2L3/EraiFisyiVbgLgrEQojZWomA0kIRjb28vWbK3d+zOCeG4n2DlT7ESFMTWRrDSxtaf4SYR0eTBwO9GWbmebHgGmz73cqNjU9MTk3P5Gfn5hcWC0vLlzpKFGVGolI1TyimeCSVYGDYLVYMRJ6gl15neOef3XNlOaRvIBuzJohaUkecErASG5huxEoQlMfn7pQ4U4bkeQZakPGT7A0i3hQzctOVneLWzaRbsPEqcH7JZKX+rn58rZ25hbeGH9EkZBKoIFrXHTuGZkoUcCpYlm8kmsWEdkiL1Q2VJGS6mfYfyvCWUXwcRMqUBNxX/06kJNS6G3qmMyTQ1sNeT/z1tv6tgqDcTLmME2CSDjYFicAQ4V482OeKURBdQwhV3ByLaZuYiMCE2EvBGf5lFyWis5ucf/cxHGEBphG62gD7SAH7aEKOkFnqIoukF36AE9WrfWvfVkPQ9ac9bPzAr6B+vlG/2hoB0=</latexit>

A21 ∼ 108 s−1 ∼ 1 s−1

<latexit sha1_base64="XyWySONoEu6hAReORWhu2+ZqXs=">ACJHicbZDLSsNAFIYn9VbjLerSzWBR3FiSUrDipurGZQV7gSYtk+m0HTqThJmJUEJ9Fze+ihsXnDhxmdx2ga0rQcGfv7vHM6c348Ylcq2v4zM0vLK6lp23dzY3NresXb3ajKMBSZVHLJQNHwkCaMBqSqGlEgiDuM1L3B9djXr8nQtIwuFPDiHgc9QLapRgpbWti8t2UnBG8Bi6knIHbtVekhcwaEctZJTVzX/KUzqG3l7Lw9KbgonFTkQFqVtvXudkIcxIozJCUTceOlJcgoShmZGS6sSQRwgPUI0tA8SJ9JLJkSN4pJ0O7IZCv0DBift3IkFcyiH3dSdHqi/n2dj8jzVj1S15CQ2iWJEATxd1YwZVCMeJwQ4VBCs21AJhQfVfIe4jgbDSuZo6BGf+5EVRK+SdYv78tpgrX6VxZMEBOAQnwAFnoAxuQAVUAQaP4Bm8gjfjyXgxPozPaWvGSGf2wUwZ3z9AV6GQ</latexit>

(permitted) (forbidden) Heisenberg uncertainty principle

∆x · ∆p & ~

<latexit sha1_base64="8KerPwWbMpl07ZIutzxSImCXMA=">ACDnicbVDLSgMxFM3UV62vUZeKBEvBVZkRQd0VdeGyBfuAzlAymbQNzTxI7ohl6NKVG3/FjRF3Lp25zf4E6aPhbYeCJycw/JPV4suAL+jIyC4tLyvZ1dza+sbmlrm9U1NRIimr0khEsuERxQPWRU4CNaIJSOBJ1jd612O/Potk4pH4Q30Y+YGpBPyNqcEtNQyC84VE0DwHXaoHwGeXmPsdECnAux0PSJbZt4qWmPgeWJPSb60P6x83x8My3z0/EjmgQsBCqIUk3bisFNiQROBRvknESxmNAe6bCmpiEJmHLT8ToDXNCKj9uR1CcEPFZ/J1ISKNUPD0ZEOiqW8k/uc1E2ifuSkP4wRYSCcPtROBIcKjbrDPJaMg+poQKrn+K6ZdIgkF3WBOl2DPrjxPasdF+6R4XtFtXKAJsmgPHaIjZKNTVELXqIyqiKIH9IRe0KvxaDwb8b7ZDRjTDO76A+Mjx+mAJ71</latexit>

(∆x c )(∆p · c) & ~ ∆t·∆E & ~

<latexit sha1_base64="bSRVNnGxFlfgT0X+1IPg8k3PxI=">ACTHicbVDLSgMxFM3Ud31VXboJFqVuyowU1J34AJcK9gFNKZnbTBvMPEjuiGXoB7px4c6vcONCEcHUzkKrFwIn5x7c3P8REmDrvsFGZm5+YXFpeKyura+uljc2GiVMNog6xinXL50YoGYk6SlSilWjBQ1+Jpn97Ntabd0IbGUc3OExEJ+T9SAYSOFqW4IKCzSHjJ0LhZzejzIY7dM9WsmJhDLoxUhn1LWRzsopGzgc0ZK+YezD17+f1iytotld2q+130L/ByUCZ5XVLT6wXQxqKCEFxY9qem2An4xolKDEqstSIhMt74u2hREPhelk32GM6K5lejSItT2RXzM/uzIeGjMPStM+Q4MNPamPxPa6cYHUyGSUpigmDwWpohjTcbK0J7UAVEMLOGhpd6Uw4DZctPkXbQje9Jf/gsZB1atVj69r5ZPTPI5Fsk12SIV45JCckEtyReoEyAN5IW/k3Xl0Xp0P53NiLTh5zxb5VYX5L34asK8=</latexit>
slide-6
SLIDE 6

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Broadened Line Shapes

6

(ν − ν0)/σ

<latexit sha1_base64="HudVlDgkiTtqQ3UZlwQENzvQOg=">AB/XicbVDLSgMxFM3UV62v8bFzE1qEilhnRFB3RTcuK9gHdIYhk6Y1NMkMSUYh+JP+AFuXCji1v9w178xfSy09cCFwzn3cu89Ycyo0o4ztHILi0vLK/nVwtr6xuaWvb3TUFEiManjiEWyFSJFGBWkrqlmpBVLgnjISDPsX4/85gORikbiTqcx8TnqCdqlGkjBfZe2RPJsanAOYQn0FO0x1Fgl5yKMwacJ+6UlKpF7+h5WE1rgf3tdSKcCI0ZkiptuvE2s+Q1BQzMih4iSIxwn3UI21DBeJE+dn4+gE8MEoHdiNpSmg4Vn9PZIgrlfLQdHKk79WsNxL/89qJ7l74GRVxonAk0XdhEdwVEUsEMlwZqlhiAsqbkV4nskEdYmsIJwZ19eZ40TivuWeXy1qRxBSbIg31QBGXgnNQBTegBuoAg0fwAt7Au/VkvVof1uekNWdNZ3bBH1hfP3WblvE=</latexit>

Lorentzian Profile (natural broadening) Gaussian Profile (realistic broadening)

slide-7
SLIDE 7

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

7

i.e., the difference b/t energy levels is NOT exact

Other Types of Broadening

  • Natural Broadening
  • Pressure Broadening
  • Zeeman Broadening

broadened Dense environments, frequent collisions induce electric fields that modify energy levels

slide-8
SLIDE 8

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Doppler Broadening

8

Thermal Broadening

slide-9
SLIDE 9

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Velocity distribution of particles in thermal equilibrium have a Maxwell-Boltzmann distribution

9

F(v)dv = 4π ⇣ m 2πkT ⌘3/2 v2 exp ✓ −mv2 2kT ◆ dv

<latexit sha1_base64="MJzhNeDrAxmoAFTYcYOtEN/yKg=">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</latexit>

F(E)dE = F(v) dv dE = 2 √πkT ✓ E kT ◆1/2 exp ✓ − E kT ◆

<latexit sha1_base64="V6IV0raS0R8lm7Sd1GaZfVP2RmA=">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</latexit>

hxi = Z xf(x)dx

<latexit sha1_base64="mflhfuhL1SCgkRUq2N8VNgjbp70=">ACnicbVC7SgNBFJ2Nrxhfq5Y2o0GITdgVRQU1QRvLCOYB2RBmJ7PJkNkHM3clIa2sfFDbCwUsfUL7PwI/8HJo9DEAxcO59zLvfe4keAKLOvLSMzMzs0vJBdTS8srq2vm+kZJhbGkrEhDEcqKSxQTPGBF4CBYJZKM+K5gZbd9OfDLt0wqHgY30I1YzSfNgHucEtBS3dx2BPgFHewI3mzBef4Ds8AC14mc4ebnTqZtrKWkPgaWKPSTqfyx7m7r4fC3Xz02mENPZAFQpaq2FUGtRyRwKlg/5cSKRYS2SZNVNQ2Iz1StN3ylj3e10sBeKHXpK4bq74ke8ZXq+q7u9Am01KQ3EP/zqjF4x7UeD6IYWEBHi7xYAjxIBfc4JREF1NCJVc34pi0hCQaeX0iHYky9Pk9J+1j7InlzrNC7QCEm0hXZQBtnoCOXRFSqgIqLoHj2hF/RqPBjPxpvxPmpNGOZTfQHxscPbPqb0g=</latexit>

hvi = r 8kT πm

<latexit sha1_base64="yCyLyYA2aHZ4iKOigQ17U5yzPx8=">ACFnicbVDJSgNBEO1xjXGLevTSGAQvhlRjLgFvegtQhYhE0NPpydp0rPYXRMIw3yFz/CH9CDB0W8ijf/xs5y0OiDgsd7VTVc0LBFZjmlzExOTU9M5uaS8vLC4tZ1ZWKyqIJGVlGohAXjtEMcF9VgYOgl2HkhHPEazqdM7frXLpOKBX4JeyOoeafnc5ZSAlhqZbVswF45wF9uSt9pwgo+xrW4lxLYrCY3zuINLSWyHtJ0shkzZw5AP5LrBHJFg4fLp9u9k6Ljcyn3Qxo5DEfqCBK1SwzhHpMJHAqWJK2I8VCQjukxWqa+sRjqh4P3krwpla2A2kLh/wQP05ERNPqZ7n6E6PQFuNe3xP68WgZuvx9wPI2A+HS5yI4EhwP2McJNLRkH0NCFUcn0rpm2i4wCdZFqHYI2/JdUdnLWbu7gSqdxhoZIoXW0gbaQhfZRAV2gIiojiu7QI3pBr8a98Wy8Ge/D1gljNLOGfsH4+AbzsqGe</latexit>

hEi = 3 2kT

<latexit sha1_base64="jIFZrndZqsoW5TfBKR+Pm8mDEo=">AC3icbVC7SgNBFJ31GeMraiFiMyQIVmE3CkZQCYpgGSEvyIYwO5lNhsw+mLkrhCW9jb9iY6GIrb3YaWPrZzh5FJp4MLhnHu59x4nFyBaX4YM7Nz8wuLiaXk8srq2npqY7OigkhSVqaBCGTNIYoJ7rMycBCsFkpGPEewqtO9GPjVGyYVD/wS9ELW8Ejb5y6nBLTUTKVtwVw4wZfYlrzdgTN8im1XEhof9ONcH3dxqZnKmFlzCDxNrDHJFPJfb9uf3zvFZurdbgU08pgPVBCl6pYZQiMmEjgVrJ+0I8VCQrukzeqa+sRjqhEPf+njPa20sBtIXT7gofp7IiaeUj3P0Z0egY6a9Abif149AjfiLkfRsB8OlrkRgJDgAfB4BaXjILoaUKo5PpWTDtEJwE6vqQOwZp8eZpUclnrMHt8rdM4RyMk0C5Ko31koSNUQFeoiMqIolt0jx7Rk3FnPBjPxsuodcYz2yhPzBefwDNs51p</latexit>
  • Avg. particle speed
  • Avg. particle

kinetic energy

slide-10
SLIDE 10

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Doppler Broadening

10

Thermal Broadening line-of-sight “velocity dispersion” (width of a Gaussian distribution)

σlos = ✓ kT µmp ◆1/2 ≈ 100 m s−1 ✓ T 1 K ◆1/2 µ−1/2

<latexit sha1_base64="sha6bIJ4r+Awp9jxNzS2Djv/YLg=">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</latexit>

∆λ λ ≈ σlos c

<latexit sha1_base64="6lByNcnbVFXusR+qy9wRo1XjhKI=">ACKnicbVDLSgMxFM34tr5GXYi4CYrgqsyIYN3Vx8JlBauFTil30kwNJpMhyYhlmO9x468I4kKpLty48DNMH4JaDwQO5zLzT1hwpk2ntd1xsYnJqemZ2YLc/MLi0vu8sqFlqkitEokl6oWgqacxbRqmOG0ligKIuT0Mrw+7vmXN1RpJuNz0loQ0A7ZhEjYKzUdA+DSAHJghPKDeCA28kW5Nk3wQEkiZK3eBjTrC2gmQVKYC51nmckb7pbXtHrA48Sf0i2yqX3x7Xz/VK030KWpKkgsaGcNC67nuJaWSgDCOc5oUg1TQBcg1tWrc0BkF1I+ufmuNtq7RwJV9scF9edEBkLrjghtUoC50n+9nvifV09NVGpkLE5SQ2MyWBSlHBuJe73hFlOUGN6xBIhi9q+YXIEtxdh2C7YE/+/Jo+Rit+jvFQ/ObBtHaIAZtIE20Q7y0T4qo1NUQVE0B16QM/oxbl3npyu8zaIjnDmVX0C87HF57WrQw=</latexit>
slide-11
SLIDE 11

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Lines are not delta functions!

11

i.e., the difference b/t energy levels is NOT exact

Motion-induced Broadening (small Doppler shifts cause lines to appear more broad)

  • Thermal Broadening
  • Rotational Broadening
  • Turbulent Broadening

broadened

slide-12
SLIDE 12

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Radiative Transfer / mfp / optical depth / Blackbody Spectra

12

slide-13
SLIDE 13

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Solar System

13

slide-14
SLIDE 14

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 14

Mass Fractions

Sun Rest

slide-15
SLIDE 15

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 15

Mass Fractions

Sun Rest Earth

slide-16
SLIDE 16

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Structure of the Sun

16

Core: ~15 million K H —> He fusion produces Sun’s photons Photons take ~100,000 years to travel through the Sun, then take 8 min to reach the Earth Temperature decreases outside the core until it falls to 5780 K at the “surface”

slide-17
SLIDE 17

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 17

Temperature & Density Profiles of the Sun

= 10-3 kg/m3

slide-18
SLIDE 18

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 18

https://www.youtube.com/watch?v=W_Scoj4HqCQ

Photons ultimately brought by convection cells

Texas ~1000 km

slide-19
SLIDE 19

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Photosphere: Limb Darkening

19

Venus

T1 T2

τ = 1

<latexit sha1_base64="0qBUcnFLQcq+ecudgEkrbWBAD0g=">AB73icbZDJSgNBEIZrXO4RT16aQyCpzAjgnoIBr14jGAWSIbQ0+lJmvQsdtcIYchLePGgiODJ/HuRXwbO8tBE39o+Pj/Krq/EQKjY7zbS0sLi2vrObW7PWNza3t/M5uTcepYrzKYhmrhk81lyLiVRQoeSNRnIa+5HW/fzXK6/dcaRFHtzhIuBfSbiQCwSgaq9FCmpIScdv5glN0xiLz4E6hcPFhl5K3L7vSzn+2OjFLQx4hk1Trpusk6GVUoWCSD+1WqnlCWZ92edNgREOuvWw875AcGqdDgliZFyEZu787MhpqPQh9UxlS7OnZbGT+lzVTDM68TERJijxik4+CVBKMyWh50hGKM5QDA5QpYWYlrEcVZWhOZJsjuLMrz0PtuOieFM9vnEL5EibKwT4cwBG4cApluIYKVIGBhAd4gmfrznq0XqzXSemCNe3Zgz+y3n8AJ7CSZw=</latexit>

T2 > T1

<latexit sha1_base64="sHV6YBeql3OIFHKE+Jb/f3pbKyA=">AB8HicbVDLSgNBEOyNrxhfUcGLl8EgeAq7QVAvEuLFYwJ5SbIs5PZMjs7DIzK4QlX+HFgyJeBf/CL/DmxW9x8jhoYkFDUdVNd5cfc6a0bX9ZmZXVtfWN7GZua3tndy+/f9BUSIJbZCIR7LtY0U5E7Shmea0HUuKQ5/Tlj+8mfiteyoVi0Rdj2LqhrgvWMAI1ka6q3sldI3qnuPlC3bRngItE2dOCuWj2jd7r3xUvfxntxeRJKRCE46V6jh2rN0US80Ip+NcN1E0xmSI+7RjqMAhVW46PXiMTo3SQ0EkTQmNpurviRSHSo1C3SGWA/UojcR/M6iQ4u3ZSJONFUkNmiIOFIR2jyPeoxSYnmI0MwkczcisgAS0y0yShnQnAWX14mzVLROS9e1UwaFZghC8dwAmfgwAWU4Raq0ACITzAEzxb0nq0XqzXWvGms8cwh9Ybz+3dZLE</latexit>

Iλ(T2) > Iλ(T1)

<latexit sha1_base64="/aCqRw8CZPgWT/0NeSnId2p2XzI=">ACnicbVDLSsNAFJ3UV62vqEs3Y4vQIpSkCOpGim50V6G1hSaEyWTSDp08mJkIXTtxqW/4caFIm79Anf9G6ePhW09MHA451zu3OPGjApGCMt7K6tr6R3yxsbe/s7un7Bw8iSjgmLRyxiHdcJAijIWlJKhnpxJygwGWk7Q5uxn7kXBo7Ap05jYAeqF1KcYSU5+vGdYzEV9xAsN51aBV7BOcWsOHrJqBoTwGVizkipXrROX0b1tOHoP5YX4SQgocQMCdE1jVjaGeKSYkaGBSsRJEZ4gHqkq2iIAiLsbHLKEJ4oxYN+xNULJZyofycyFAiRBq5KBkj2xaI3Fv/zuon0L+yMhnEiSYini/yEQRnBcS/Qo5xgyVJFEOZU/RXiPuIS9VeQZVgLp68TB5qVfOsenmv2rgGU+TBESiCMjDBOaiDW9ALYDBE3gF7+BDe9betE/taxrNabOZQzAH7fsXJPWa/w=</latexit>
slide-20
SLIDE 20

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03

Corona: high T allows particles to reach vesc

20

t ∼ 5 × 109 yr

<latexit sha1_base64="GCukIcQ8OXeVMCzuBUrn7s63cyA=">ACDnicbVA9SwNBEN3z2/gVtbRZDYHYhDtRNF3QxlLBJEIuhr3NXrJk9/bYnRPCEf+Ahf4VGwtFBCtrO3+IvZvEQhMfDzem2FmXhALbsB1P52p6ZnZufmFxczS8srqWnZ9o2pUoimrUCWUvgyIYJHrAIcBLuMNSMyEKwWdE8Gfu2acNVdAG9mDUkaUc85JSAlZrZPDR91VKAfcMlPsA+cMkM9tyrtNS/SX0tcU/3m9mcW3SHwJPE+yG58nbh6+3O3z1rZj/8lqKJZBFQYype24MjZRo4FSwfsZPDIsJ7ZI2q1saEbu0kQ7f6eO8Vo4VNpWBHio/p5IiTSmJwPbKQl0zLg3EP/z6gmER42UR3ECLKjRWEiMCg8yAa3uGYURM8SQjW3t2LaIZpQsAlmbAje+MuTpLpX9PaLpXObxjEaYQFtoR1UQB46RGV0is5QBVF0ix7QE3p27p1H58V5HbVOT8zm+gPnPdvnqe4g=</latexit>

˙ M ∼ 108 kg/s ∼ 1014 M/yr

<latexit sha1_base64="GOc/lbz90X9MZLOtvu6VcLloXjk=">ACK3icbVDLSgMxFM3UV62vUZdugkVxYzsjBeu1I2bQgX7gE4tmTRtQ5OZIckIwzB+jxt/xYUufODW/zBtB9TWA4HDOfdwc48bMCqVZb0bmaXldW17HpuY3Nre8fc3WtKPxSYNLDPfNF2kSMeqShqGKkHQiCuMtIyx1fTvzWHRGS+t6NigLS5Wjo0QHFSGmpZ1advq/iWgKPHUk5tK3buJzcx47gcDwsysRxcj/OqV1KvVrP8XUQFiOR9My8VbCmgIvETkepKj3zGe9FIeceAozJGXHtgLVjZFQFDOS5JxQkgDhMRqSjqYe4kR24+mtCTzSh8OfKGfp+BU/Z2IEZcy4q6e5EiN5Lw3Ef/zOqEalLsx9YJQEQ/PFg1CBpUPJ8XBPhUEKxZpgrCg+q8Qj5BAWOl6c7oEe/7kRdI8K9ilwsV1KV+pnVkwQE4BCfABuegAq5AHTQABg/gCbyCN+PReDE+jM/ZaMZIM/vgD4yvb76vpjE=</latexit>
slide-21
SLIDE 21

ASTR/PHYS 2500: Foundations Astronomy Fall 2020: Week 03 21

Mass Fractions

Sun Rest Saturn Jupiter