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