phy 53 lecture		dr. brown		2 november 2010

grade reassurance    mean = 65  

more gravity

\vec{F} = -\frac{G M m}{r^2} \hat{r}

issue  = non-contact force  ; Newton invents a "field"  to explain this

\vec{g} = \frac{\vec{F}}{m} = \frac{-G M}{r^2} 

really important -- would be better to say only fields exert forces than to talk about "contact" forces

gravitational fields satisfy the superposition principle

example -- find gravitational field at a point on the x-axis due to two masses which are at +a and -a onthe y-axis

there exist a number of ways to represent a vector solution -- pick one and use it -- ie. you must show both magnitude and direction [all components, magnitude and picture, magnitude and clear words, polar coordinates, ...]

what about continuous distributions of mass ... integrals ... not going to force this class to do these -- but you must believe some presented facts

1. spherical ball of mass --  field outside a spherically symmetric mas is the same as that of a point mass at the center

R_{earth} approx 4000 miles or approx 6400 km
G = 6.67 \times 10^{-11}
g approx 10
so you can find M_{earth}

2. inside a spherical shell, gravitational field = o

so... you can solve homework problem...#4 ;  does this example
gravitational field inside earth at radius r

g_r = \frac{G m}{R^3} r ;   linear in r


We would like to work with with scalars -- potential, work, energy

Define change in gravitational potential
\Delta U = - \frac{GMm}{r_1} + \frac{GMm}{r_0}

define U(\infty} = 0
U(\vec{r}) = - \frac{GMm}{r}

Now two dimentional motion in gravitational field

defines U_{effective}
and does hwk prob with U_{effective} graph -- identify circular, elliptical, parabolic, and hyperbolic curves

Escape velocity or escape energy E_{tot} >= 0

approx 11km/s