AST-101, Ast-117, AST-602 · 2019. 9. 17. · Stars and Galaxies Luis Anchordoqui AST-101, Ast-117, AST-602 1 101_4 - September 17, 2019

Stars and GalaxiesLuis Anchordoqui

AST-101, Ast-117, AST-602

1 101_4 - September 17, 2019

2 101_4 - September 17, 2019

Newton’s Second Law of Motion

•  The force law –  The acceleration of an object is directly proportional to the

net force acting on it and is inversely proportional to its mass

•  Force = Mass x Acceleration –  The harder you push on something the faster it will

accelerate –  If a force is applied to an object of large mass is will

accelerate more slowly than an object of smaller mass with the same force

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Newton’s Law of Universal Gravitation

•  Two objects attract each other with a force (F) –  directly proportional to the product of their masses (M and m) –  inversely proportional to the square of the distance (r)

between them

mgd

GMmFgravity == 2 2d

GMg =

•  Weight on earth = Gravitational Force •  m – your mass in unit of kg •  M – mass of Earth = 5.97 x 10 24 kg •  G – Universal gravitational constant = 6.67 x 10-11 m3kg-1s-2 •  r – Earth s radius = 6.37 x 106 m

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Satellite Motion

𝐹𝑥 = 𝐹𝑔𝑟𝑎𝑣,𝑥 = 𝑚𝑠𝑎𝑡𝑎𝑥=𝑚𝑠𝑎𝑡(+𝑎𝐶)

𝐺𝑚𝑠𝑎𝑡𝑀𝑅2

= 𝑚𝑠𝑎𝑡𝑣2

𝑅

𝐺𝑀𝑅= 𝑣2 =

2π𝑅𝑇

2

𝑇2 =4π2

𝐺𝑀𝑅3 Kepler’s 3rd Law

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Find mass of Earth

𝑀𝐸𝑎𝑟𝑡ℎ =𝑔𝑅𝐸𝑎𝑟𝑡ℎ2

𝐺

𝑔 =𝐺𝑀𝐸𝑎𝑟𝑡ℎ𝑅𝐸𝑎𝑟𝑡ℎ2

If 𝐺 and 𝑅𝐸𝑎𝑟𝑡ℎ known:

𝐺: Cavendish balance

𝑅𝐸: Eratosthenes 200BC

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l

l =1

2gt2 T = 2⇡

sl

g

T ! period of pendulum

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8/31/19, 4)24 PM30 September

Page 2 of 4https://www.eg.bucknell.edu/physics/astronomy/astr101/calpages/30sep05.html

What's wrong with the other planets?Are these special traits permanent, or will the Earth become (or can we make itby accident) hostile to life?

Understanding the Earth's Interior

Lots down there,We can't access it.Need to use remote sensing meansTwo important ways -- density and seismology.

What We Can Learn from the Density of the Earth

Density = mass/ volume, so we'll need mass and volume.Get mass from watching the speed and orbit size of a satellite (Moon orartificial).Get volume from V = 4/3 x pi x r3, where r is the radius of the Earth and weassume it's a sphere (close enough).Earth's average density is 5480 kg/m3.Compares with densities of other materials.Gold: 19300 kg/m3 Lead: 11400 kg/m3 Iron: 7900 kg/m3 Rock: 2500 kg/m3 Water: 1000 kg/m3 Ice: 920 kg/m3 Wood: 800 kg/m3 Good bet iron and rock are major constituents of the Earth.Even more, since we know that the Earth's surface is mainly rocky, with arock-type density, the we can conclude that the deep interior must be evenmore dense (to make the average as big as 5480 kg/m3). 8/31/19, 4)24 PM30 September


Thus, we know that the core of the Earth must be iron-rich.And we know that the Earth is differentiated, i.e., the heavy stuff is at thecenter and the lighter stuff is on the surface.That means the Earth was once pretty molten (since stuff had to be able tomove around to differentiate).The Earth must've had a hot period in its early history.

Using Seismology to Map the Earth's Interior

Earthquakes generate waves that travel through the Earth."P" waves are compression waves, and travel through just about anything."S" waves are more like "wiggles" on a string; they don't propagate throughliquids.Types of waves detected at sites on the other side of the Earth from anearthquake tell us something about the material through which the wavespassed.The absence of "S" waves in these kinds of experiments tells us that some partof the Earth's core is liquid.

Why is the Earth's Center Hot?

The fact that some of the Earth's interior is liquid implies that it's hot.Temperature at center > 5000K.Heat from formation of the Earth; impacts and the proto-Earth coalesced.Heat from radioactive decay.

Convection and Plate Tectonics

Hot in the center, cool on the outside --> recipe for convection.Hot stuff rises, cool stuff falls.Creates convective "rolls" -- plumes of hot upward-moving stuff surrounded bycooler descending material.Happens very slowly in the gummy sticky mantle material.

8/31/19, 4)24 PM30 September


What's wrong with the other planets?Are these special traits permanent, or will the Earth become (or can we make itby accident) hostile to life?

Understanding the Earth's Interior

Lots down there,We can't access it.Need to use remote sensing meansTwo important ways -- density and seismology.

What We Can Learn from the Density of the Earth

Density = mass/ volume, so we'll need mass and volume.Get mass from watching the speed and orbit size of a satellite (Moon orartificial).Get volume from V = 4/3 x pi x r3, where r is the radius of the Earth and weassume it's a sphere (close enough).Earth's average density is 5480 kg/m3.Compares with densities of other materials.Gold: 19300 kg/m3 Lead: 11400 kg/m3 Iron: 7900 kg/m3 Rock: 2500 kg/m3 Water: 1000 kg/m3 Ice: 920 kg/m3 Wood: 800 kg/m3 Good bet iron and rock are major constituents of the Earth.Even more, since we know that the Earth's surface is mainly rocky, with arock-type density, the we can conclude that the deep interior must be evenmore dense (to make the average as big as 5480 kg/m3).

9 101_4 - September 17, 2019

Across the Universe Stars and Galaxies

Night sky provides a strong impression of a changeless universe

G Clouds drift across the Moon + on longer times Moon itself grows and shrinksG Moon and planets move against the background of starsG These are merely local phenomena caused by motions within our solar systemG Far beyond planets + stars appear motionless

L. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 3 / 19

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Impression of changelessness star background is illusory

Barnard's Star

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Distances involved are so large that we specify themin terms of the time it takes the light to travel a given distance

light second + 1 ls = 1 s 3 ⇥ 108 m/s = 3 ⇥ 108m = 300, 000 kmlight minute + 1 lm = 18 ⇥ 106 kmlight year + 1 ly = 2.998 ⇥ 108 m/s · 3.156 ⇥ 107 s/yr

= 9.46 ⇥ 1015 m ⇡ 1013 kmHow long would it take the space shuttle to go 1 ly?

Shuttle orbits Earth @ 18,000 mph + it would need 37, 200 yrL. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 6 / 19

13 101_4 - September 17, 2019


For specifying distances to Sun and Moon we usually use km

but we could specify them in terms of lightEarth-Moon distance is 384,000 km + 1.28 ls.Earth-Sun distance is 150,000,000 km + 8.3 lmFar out in the solar systemPluto is about 6 ⇥ 109 km from the Sun + 6 ⇥ 10�4 lyNearest star to us + Proxima Centauri is about 4.3 ly awayNearest star is 10,000 times farther from us

than outer reach of solar system

L. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 7 / 1914 101_4 - September 17, 2019

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Potential for primitive life on icy Barnard b super-earth planet if geothermal activity exists

I Ribas et al., Nature 563 (2018) 365

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On clear moonless nights thousands of stars with varying degrees of brightnesscan be seen + as well as the long cloudy strip known as Milky Way

Galileo first observed with his telescope that Milky Wayis comprised of countless numbers of individual stars

Half century later (about 1750) Thomas Wright suggested that Milky Waywas a flat disc of stars extending to great distances in a plane

which we call Galaxy (Greek for “milky way”)

Milky Way over Quiver Tree Forest in southern Namibia



Galaxy has diameter ⇠ 100, 000 ly and thickness ⇠ 2, 000 lyIt has a bulging central “nucleus” and spiral armsOur Sun is located half way from the Galactic center to the edge

some 26, 000 ly from the centerL. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 9 / 19

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G Sun orbits Galactic center about once every 250 million yearsG its speed is Ù

v =2p 26, 000 ⇥ 1013 km

2.5 ⇥ 108 yr 3.156 ⇥ 107 s/yr = 200 km/s

G Total mass of all stars can be estimated using orbital data of SunG Assume most of the mass is concentrated near center of GalaxyG Sun and solar system (of total mass m)

move in circular orbit around Galaxy center (of total mass M)G Apply Newton’s laws

GMm

r2= m

v2

r

G = 6.674 ⇥ 10�11 N m2 kg�2

M =r v

2

G⇡ 2 ⇥ 1041 kg

G Assuming all stars in Galaxy are similar to Sun (M� ⇡ 2 ⇥ 1030 kg)we conclude that there are roughly 1011 stars in the GalaxyL. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 10 / 19

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In addition to stars we can see with telescopemany faint cloudy patches that were once called “nebulae”

Those in the constellations of Andromeda and Orioncan actually be discerned with naked eye on clear night

At first it was not universally acceptedthat these objects were extragalactic

Very large telescopes constructed in XX centuryresolved individual stars within these extragalactic objects

that also contain spiral armsIt became logical that nebulae must be galaxies similar to oursDistance to nearest spiral galaxy + Andromeda over 2 million lya distance 20 times greater than the diameter of our GalaxyToday it is thought there are ⇠ 4 ⇥ 1010 galaxies

that is as many galaxies as there are stars in the Galaxy



Deep field of view as seen by Hubble Space Telescope1.3 Black-body radiation

Figure 1.2: An excerpt from the Deep Field View taken by the Hubble Space Telescope.

1.3.1 Kirchho�-Planck distribution

Planck found empirically 1900 the so-called Kirchho�-Planck (or simply Planck) distribution

B�d� =2h�3

c21

exp( h�kT ) � 1d� (1.6)

describing the amount of energy emitted into the frequency interval [�, � + d�] and the solidangle d� per unit time and area by a body in thermal equilibrium. The function B� dependsonly on the temperature T of the body (apart from the natural constants k, c and h) and isshown in Fig. 1.4 for di�erent temperature T . The dimension of B� in the cgs system of unitsis

[B� ] =erg

Hz cm2 s sr. (1.7)

In general, the amount of energy per frequency interval [�, � +d�] and solid angle d� crossingthe perpendicular area A� per time is called the (di�erential) intensity I� , cf. Fig. 1.3,

I� =dE

d� d� dA� dt. (1.8)

For the special case of the blackbody radiation, the di�erential intensity is given by theKirchho�-Planck distribution, I� = B� .

Equation (1.6) gives the spectral distribution of black-body radiation as function of thefrequency �. In order to obtain the corresponding formula as function of the wavelength �,one has to re-express both B� and d�: With � = c/� and thus d� = �c/�2d�, it follows

B�d� =2hc2

�51

exp( hc�kT ) � 1d� . (1.9)

13

L. A. Anchordoqui (CUNY) Conceptual Physics 12-5-2017 12 / 19

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AST-101, Ast-117, AST-602 · 2019. 9. 17. · Stars and Galaxies Luis Anchordoqui AST-101, Ast-117, AST-602 1 101_4 - September 17, 2019