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10/10/2013PHY 113 C Fall 2013-- Lecture 131PHY 113 C General Physics I11 AM - 12:15 PM MWF Olin 101

Plan for Lecture 13:Chapter 13 Fundamental gravitational force law and planetary motionGravitational force law; relationship with g near Earths surfaceOrbital motion of planets, satellites, etc.Energy associated with gravitation and planetary motionProblems 1.1,1.6,1.10,1.11110/10/2013PHY 113 C Fall 2013-- Lecture 132

210/10/2013PHY 113 C Fall 2013-- Lecture 133Question from Webassign Assignment #11

10/10/2013PHY 113 C Fall 2013-- Lecture 134

Xt1t3t2

10/10/2013PHY 113 C Fall 2013-- Lecture 135

Xt1t3t2

10/10/2013PHY 113 C Fall 2013-- Lecture 136

Question from Webassign Assignment #11X

10/10/2013PHY 113 C Fall 2013-- Lecture 137

Question from Webassign Assignment #11

iclicker question: A. Ki=Kf ? B. Ki=Kf ? 10/10/2013PHY 113 C Fall 2013-- Lecture 138Universal law of gravitation Newton (with help from Galileo, Kepler, etc.) 1687

10/10/2013PHY 113 C Fall 2013-- Lecture 139Newtons law of gravitation: m2 attracts m1 according to:

xym1m2r2r1r2-r1

G=6.67 x 10-11 N m2/kg2

F1210/10/2013PHY 113 C Fall 2013-- Lecture 1310Vector nature of Gravitational law:m1m2m3xydd

F1310/10/2013PHY 113 C Fall 2013-- Lecture 1311Gravitational force of the Earth

REm

Note: Earths gravity acts as a point mass located at the Earths center.10/10/2013PHY 113 C Fall 2013-- Lecture 1312Question: Suppose you are flying in an airplane at an altitude of 35000ft~11km above the Earths surface. What is the acceleration due to Earths gravity?

a/g = 0.99710/10/2013PHY 113 C Fall 2013-- Lecture 1313Attraction of moon to the Earth:

Acceleration of moon toward the Earth:F = MM a a = 1.99x2020 N/7.36x1022kg =0.0027 m/s2REM10/10/2013PHY 113 C Fall 2013-- Lecture 1314

10/10/2013PHY 113 C Fall 2013-- Lecture 1315Gravity on the surface of the moon

Gravity on the surface of mars

10/10/2013PHY 113 C Fall 2013-- Lecture 1316iclicker question:In estimating the gravitational acceleration near the surfaces of the Earth, Moon, or Mars, we used the full mass of the planet or moon, ignoring the shape of its distribution. This is a reasonable approximation because:The special form of the gravitational force law makes this mathematically correct.Most of the mass of the planets/moon is actually concentrated near the center of the planet/moon.It is a very crude approximation.

10/10/2013PHY 113 C Fall 2013-- Lecture 1317

Stable circular orbit of two gravitationally attracted objects (such as the moon and the Earth)

REMFav10/10/2013PHY 113 C Fall 2013-- Lecture 1318iclicker question:In the previous discussion, we saw how the moon orbits the Earth in a stable circular orbit because of the radial gravitational attraction of the moon and Newtons second law: F=ma, where a is the centripetal acceleration of the moon in its circular orbit. Is this the same mechanism which stabilizes airplane travel? Assume that a typical cruising altitude of an airplane is 11 km above the Earths surface and that the Earths radius is 6370 km.

(a) Yes (b) No10/10/2013PHY 113 C Fall 2013-- Lecture 1319

Stable (??) circular orbit of two gravitationally attracted objects (such as the airplane and the Earth)

REaFav10/10/2013PHY 113 C Fall 2013-- Lecture 1320

Newtons law of gravitation:Earths gravity:

Stable circular orbits of gravitational attracted objects:

REm

REMFavMMSummary:10/10/2013PHY 113 C Fall 2013-- Lecture 1321More detailsIf we examine the circular orbit more carefully, we find that the correct analysis is that the stable circular orbit of two gravitationally attracted masses is about their center of mass.m1R2R1m2

10/10/2013PHY 113 C Fall 2013-- Lecture 1322m1R2R1m2Radial forces on m1:

T2 ?10/10/2013PHY 113 C Fall 2013-- Lecture 1323iclicker question:What is the relationship between the periods T1 and T2 of the two gravitationally attracted objects rotating about their center of mass? (Assume that m1 < m2.) (A) T1=T2 (B) T1T2 m1R2R1m2

10/10/2013PHY 113 C Fall 2013-- Lecture 1324m1R2R1m2

10/10/2013PHY 113 C Fall 2013-- Lecture 1325iclicker questions:How is it possible that all of these relations are equal?Magic.Trick.Algebra.

10/10/2013PHY 113 C Fall 2013-- Lecture 1326m1R2R1m2For m2>>m1 R2