Astro 1 - Lecture 5


Matthew A. Bershady

Department of Astronomy & Astrophysics

Penn State University


Fall 1996

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© 1995 Matthew A. Bershady

Lectures Lecture page Astro1 page


OF GRAVITY AND LIGHT


1. Kepler's Laws of Planetary Motion


A precise mathematical description of Tycho Brahe's accurate planetary observations.

(i) The orbital paths of the planets are elliptical, with the Sun at one foci

(ii) Equals areas of the ellipse are swept out in equal intervals of time during a planet's orbit

(iii) The square of the orbital period is proportional to the cube of the orbital semi-major axis.

Period (P):

the time it takes for the planet to orbit once (360 degrees) around the ellipse

Semi-major axis (a):

half (semi) of the longest (major) line that can be drawn through an ellipse.

One limit of an ellipse is a circle; then a is the same as the radius.

Where's the physics ?


2. Newton's Laws of Motion and Gravitation


A physical theory for how matter interacts

(i) Every body continues in a state of rest or in uniform motion unless acted on by a force

(ii) When a force acts on a body of mass M, it produces an acceleration A equal to the force F divided by the mass M.

F = M A

(iii) To very action there is an equal and opposite reaction

Concepts:

Force - F

Mass - M

Acceleration - A



3. Gravity


Masses attract!

Gravity is one of 4 forces known in nature:

FORCE CARRIER
gravitational gravitational waves, or gravitons
electro-magnetic light waves, or photons
weak W and Z particles
strong gluons


Gravitational force (the law of gravity):


Imagine two objects of different mass:

Object #1 has mass

Object #2 has mass

The two objects are separated by distance R


What's the gravitational force that they each exert on the other?

F = G / R 2


Why?


G is a universal constant, but there is currently no theory for why it has the particular value we observe

But the rest is just Newton's 2nd law:

F = G / R 2

... or ...

F = G / R 2

and simple geometry!

F 1 / R 2



4. Orbital Motion


Competition between inertia (Newton's 1st law) and the force of gravity

suborbital velocity

orbital velocity

escape velocity


A grand analogy:

The expansion of the Universe!

Will it collapse, or expand out forever?



a ton of bricks a ton of feathers

Which is more massive?

Which would weigh more on the Moon?

Would the mass of the feathers change if taken to the Moon?

Would the mass of the bricks change if taken to the Moon?

Would their weight change?


Q5.1 Which is more massive: A ton of bricks on the Earth or a ton of feathers on the Moon?

(a) the same

(b) it depends on the phase of the Moon

(c) it depends on the kind of feathers

(d) the feathers

(e) the bricks


Lectures Lecture page Astro1 page
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Last updated: Aug 28, 1996 Matthew A. Bershady