Chapter 4



Orbits and Gravity

Greek Astronomy:


Originally: Earth flat, sky a dome


After 700 B.C.: Spherical universe, spherical earth


Stars, planets, etc. in sphere(s) revolving around earth (celestial sphere)
Aristotle: Supported geocentric model of the universe. Earth at center. Earth spherical


Aristarchus: Heliocentric model (sun at center).


Parallax: Apparent change in position of an object against a background, due to the change in location of observer.


Greeks did not observe parallax, required by heliocentric model


Ptolemy's model of geocentric universe:
Earth at center


Planets, sun, etc. move at uniform rate, in perfect circles - perfect motion for heavenly bodies.


Retrograde: Apparent backward motion on the sky




Copernican Revolution:


Copernicus: 1473 - 1543


Earth revolves around the sun.


Galileo Galilei: 1564 - 1642


Observations in support of Copernicus' theory:


1. Venus' phases


2. Jupiter and its moons


3. "Imperfections" on the sun and moon


Tycho Brahe: 1546 - 1601


Precise observations supported Copernican view.


Tycho's supernova:


nova : "new star"


Johannes Kepler: 1571 - 1630


Used Tycho's observations to try to understand motion of planets.


Laws of Planetary Motion: empirical


1. Orbits of planets are ellipses.


2. Sun - planet line sweeps out equal area in equal time intervals. (Planet moves faster at perihelion and slower at aphelion.)


3. Planet's orbital period squared is proportional to its mean distance from sun, cubed:


P2(yr) = a3(AU)
ex.:




ex.: Saturn, (P = 29.5 years)


Measuring the Solar System


Need:


1.Relative distances of planets from the sun (get from trigonometry)


2. Value of astronomical unit


To measure AU: measure parallax angle of planet and distance between observers on earth


Get distance to any planet, if distance from sun in AU is known and get value of 1 AU


First attempt to measure 1 AU, 1672 - Mars


Now use radar - very accurate




Newtonian Gravitation

Isaac Newton (1642 - 1727)


Every body in universe attracts every other with a force depending on masses and distance between bodies.


Law of Gravity:

Where,
G: gravitational constant
M: mass of larger body
m: mass of smaller body
r: distance between bodies


Mass: amount of material in body

Weight: depends on gravitational force acting on body



Newton's Laws:

1. Newton's First Law: Body in motion remains in motion unless acted on by an outside force


Force: Can cause change in speed, direction or both.


Velocity: Speed in a particular direction.


Acceleration:Change in velocity.


2. Newton's Second Law:


mass, m acceleration, a force, F
m = 1.5 a = 2 F = 3
m = 1.5 a = 4 F = 6




3. Newton's Third Law: Every action has an equal and opposite reaction.


The acceleration due to gravity is the same for all objects in a particular gravitational field.


Acceleration due to gravity at earth's surface:


seconds speed (ft/sec) speed (m/sec)
1 32 9.8
2 64 19.6
3 96 29.4
4 128 39.2
5 160 49.0


g: acceleration due to gravity, 32 ft/s/s, or 9.8 m/s/s


Orbits

Sensation of weight - resisting force of gravity


Falling freely - not resisting gravity - feel 'weightless' BUT GRAVITY IS STILL THERE


Inside closed spaceship - cannot differentiate free fall near a planet or 'floating around' far from all sources of gravity (masses)


Escape velocity - smallest velocity required to leave earth (or any other body) and not return


Circular velocity - velocity required to orbit earth (or any other body) at a constant altitude, i.e. in a circular orbit. Ignoring air resistance, will orbit indefinitely.


Speeds greater than circular velocity produce elliptical orbits.


Escape velocity produces parabolic orbits


Speeds greater than escape velocity produce hyperbolic orbits.








Einstein, Gravity, and Relativity

Velocity of electromagnetic radiation is constant, regardless of observer's velocity relative to source. (Michelson - Morley experiment)


E = mc2


Gravity as a distortion of space near massive bodies


The more massive the body, the greater the distortion


Space and time linked in a 4 dimensional description of the universe (space-time) and how things move in it


Confirmation of General Relativity:


1. Precession of Mercury's orbit:
























2. Deflection of starlight near large masses - gravitational lenses:














All tested predictions of General Relativity confirmed thus far.


Under everyday circumstances, Newton's gravity and Einstein's relativity give same result.


Relativity must be used


1.at velocities approaching speed of electromagnetic radiation ("light")


2. when very strong gravitational fields are present


3. when considering the large-scale universe.




Prof. Donna Weistrop

University of Nevada, Las Vegas