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