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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Matter & Gravity

Readings: Ch 5, section 5-7, Ch 4, sections 4-7 & 4-8

Key Ideas

Structure of Atoms
Nuclei of protons & neutrons orbited by electrons
Elements, Isotopes, & Radioactivity

Four Fundamental Forces
Strong & Weak Nuclear Forces
Electromagnetic & Gravitational Forces

Nature of Gravity
Inverse Square Law
Orbits & Circular Speed
Escape Speed & Gravitational Binding Energy

Matter

Ordinary matter encompasses a wide range of phenomena: Most ordinary matter in the universe is in the form of atoms.

Atoms

Atoms consist of two basic parts:

Nucleus of heavy subatomic particles:

Cloud of Electrons orbiting the Nucleus:

Atoms are mostly empty space:

A simple, yet familiar cartoon:
Simple Atoms (Schematic)
Real atoms don't look like this, but it can help you visualize the locations and numbers of the different components (nucleus and electrons).

Chemical Elements

We distinguish atoms into Elements by the total number of protons in their nucleus.

Atomic Number:

Number of electrons = Number of protons

All elements are Chemically Distinct


Top Ten Most Abundant Elements

10) Sulfur
9) Magnesium
8) Iron
7) Silicon
6) Nitrogen
5) Neon
4) Carbon
3) Oxygen
2) Helium
1) Hydrogen
In general, the ordinary matter in the Universe is mostly Hydrogen and Helium (roughly 75% and 24%, respectively), and 1% every other element.

Known Elements

There are 117 elements currently known from laboratory studies:

In addition, each element can have a number of isotopes.

The two newest members of the table of the elements, with atomic numbers of 113 and 115, were recently made in accelerators in Russia.


Isotopes

A given element can have many different Isotopes

Example: Carbon Isotopes:

12C has 6 protons and 6 neutrons
13C has 6 protons and 7 neutrons
14C has 6 protons and 8 neutrons

All isotopes of a given element are chemically identical, but they have different masses.


Radioactivity

If a nucleus has too many or too few neutrons, it becomes unstable to radioactive decay

Examples:

    3H (1p+2n) -> 3He (2p+1n) + e- + neutrino

    14C (6p+8n) -> 14N (7p+7n) + e- + neutrino 
                      (basis of radioactive carbon dating)

Free neutrons are also unstable:

    n -> p + e- + neutrino

All of the above are examples of "beta decay", in which one of the neutrons turns into a proton, shedding its excess mass by spitting out an electron and a neutrino.


The Fundamental Forces

All interactions among matter are governed by four fundamental forces:
Strong & Weak Nuclear Forces
Bind protons to neutrons inside nuclei
Mediate nuclear reactions and radioactivity

Electromagnetic Force
Binds electrons to nuclei inside atoms, and atoms to atoms inside molecules
Mediates chemical reactions

Gravitational Force
Binds massive objects together on large scales
Mediates orbital motions

Gravitation

Gravitation binds matter to matter over long distances:

Gravitational Force

The Force of Gravity between any two objects depends only upon:

The masses of the two objects:

The distance between them:

It does not depend on the shapes, colors, or compositions of the objects.


Kepler's Third Law

Kepler's 3rd (or "Harmonic") Law of orbital motions
P2 = a3
only applies to planets orbiting our Sun.

Newton, however, derived a more general version

Generalized Kepler third law
This is a universal form of Kepler's 3rd law applicable to any two massive objects orbiting each other anywhere in the Universe.
The important quantities in this form are:
P = period of the orbit
a = semi-major axis of the orbit
M1+M2 = combined masses of the two bodies
This gives us a way of measuring the masses of objects from observation of their orbital period and semi-major axis.

Circular Speed

In the simple case of a tiny mass in a circular orbit around a more massive body we can simplify the formula above to define the smaller object's Circular Speed:
Circular Speed
Speed needed to sustain a circular orbit at a given distance from a massive object:
Circular Speed

The circular speed depends on two things:

This gives us another way to measure masses for objects in circular orbits around larger bodies, now measuring orbital speeds (Doppler Effect) and orbital radii.

In general, orbital motions are the most important way we have to estimate the masses of astronomical objects.


Escape Speed

Another consequence of gravitating bodies is that there is a minimum speed an object must be given in order for it to escape from the gravity of its parent body.

This is called the Escape Speed:

escape speed
The escape speed depends on the Mass of the body (M) and its radius (R). Basically, the stronger the gravity at the surface of a body, the faster you have to be going to escape from its gravitational clutches.

Examples:

Earth's Surface
Vesc = 11.2 km/sec (40,320 km/hr)
Sun's Surface
Vesc = 615 km/sec (~2.2 Million km/hr)

Gravitational Binding Energy

Imagine you wanted to take apart a gravitating body. You might do it piece-by-piece, taking a rock and throwing it with the escape speed. As the body got steadily smaller, the escape speed would be less.

If you added up all the energy you would need for each piece, you would derive the Gravitational Binding Energy for the body:

gravitational binding energy
This depends on two quantities: the Mass (M) and the Radius (R) of the body.

The formula above is a "proportionality", it tells us how the binding energy scales with the mass and radius of the object. The constant out front we need depends on details of how matter is distributed in the object. For example, a sphere of uniform density would have a constant of 3/5.

For the Earth, the Gravitational Binding Energy is about 2x1032 Joules, or about 12 days of the Sun's total energy output!

Implications

For objects of the same Radius but with different masses, the more massive object will have

For objects of the same Mass but different Radii, the larger object (bigger radius) will have:


Gravity: The Universal Glue

Gravity is the force that rules in the domain of astrophysics: Throughout this course we will be exploring the consequences of gravitation.
Return to [ Introduction Index | Astronomy 162 Main Page ]
Updated: 2006 January 4
Copyright Richard W. Pogge, All Rights Reserved.