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)

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

Apparent backward motion on the sky__Retrograde__:

__Copernican Revolution__:- Copernicus: 1473 - 1543
- Earth revolves around the sun.

1564 - 1642__Galileo Galilei__:- Observations in support of Copernicus' theory:
- 1. Venus' phases
- 2. Jupiter and its moons
- 3. "Imperfections" on the sun and moon

1546 - 1601__Tycho Brahe__:- Precise observations supported Copernican view.
- Tycho's supernova:
- nova : "new star"

1571 - 1630__Johannes Kepler__:- 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:
- P
^{2}(yr) = a^{3}(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
- Isaac Newton (1642 - 1727)
- Every body in universe attracts every other with a force depending on masses and distance between bodies.
**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
- 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:* - 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:
*g*: acceleration due to gravity, 32 ft/s/s, or 9.8 m/s/s- 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.
- Velocity of electromagnetic radiation is constant, regardless of observer's velocity relative to source. (Michelson - Morley experiment)
- E = mc
^{2} - 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.

__Law of Gravity__:

mass, m |
acceleration, a |
force, F |

m = 1.5 |
a = 2 |
F = 3 |

m = 1.5 |
a = 4 |
F = 6 |

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 |

*Prof. Donna Weistrop*

*University of Nevada, Las Vegas*