Announcementsp FINAL EXAM

n PHYS 131-001: Wednesday, 12/13 @ 8-9:50 amn PHYS 131-002: Monday, 12/11 @ 10-11:50 am

p Homework for tomorrow…(Ch. 13: Probs. 28, 34, & 40)

CQ2: 2CQ3: a) ½ b) 113.2: 2.2 13.6: 3.0 x 1011 m

p Office hours…MW 1-2pmTF 11-12pmR 9-10am

p Tutorial Learning Center – Houston Hall 113M 8-6pm R 8-1:30pm, 3:30-6pm

T 8-1:30pm, 2-6pm F 8-11am, 12-5pmW 8-11am, 1-6pm SU 1-6pm

Timeline…p Today: Chapter 13, Lecture 3

p Wednesday: Post-Diagnostic Exam + Evaluations

p Friday: Final Exam Review + Cards

p FINAL EXAM:n PHYS 131-001: Wednesday, 12/13 @ 8-9:50 amn PHYS 131-002: Monday, 12/11 @ 10-11:50 am

Chapter 13

Newton’s Theory of Gravity(Satellite Orbits and Energies)

Gravitational Potential Energy…

Review…

U(r) = �Gm1m2

r

Quiz Question 1Which system has more (larger absolute value)

gravitational potential energy?

1. System A2. System B3. They have the same gravitational potential energy.

Quiz Question 2An object is dropped from an altitude of one Earth radius

above the Earth’s surface. If M is the mass of the Earth and R is its radius, then the speed of the object just before it hits Earth is (ignoring air resistance):

(Hint: Consider Conservation of Mechanical Energy)

1.

2.

3.

4.

5.

pGM/R

pGM/2Rp2GM/R

pGM/R2

pGM/2R2

A Little History: Kepler’s Lawsp From 1570 to 1600, Tycho Brahe compiled observations

of stars and planets, and noted how the planets Mercury, Venus, Mars, Jupiter, and Saturn move through the sky.

p His mathematical assistant, Johannes Kepler, analyzed Brahe’s data and discovered three laws that the planets obey as they orbit the sun.

Kepler’s 1st Law…K1L: Planets move in elliptical orbits, with the sun at one

focus of the ellipse.

Kepler’s 2nd Law…K2L: A line drawn between the sun and a planet sweeps out

equal areas during equal time intervals.

Kepler’s 3rd Law…K3L: The square of a planet’s orbital period is proportional

to the cube of the semimajor-axis length.

Mathematically:

Kepler’s 3rd Law…K3L: The square of a planet’s orbital period is proportional

to the cube of the semimajor-axis length.

Mathematically:

T 2 =

✓4⇡2

GM

◆r3

Quiz Question 3The moon does not crash into the Earth because:

1. The net force on it is zero2. It is beyond the pull of Earth’s gravity3. It is being pulled away by the sun and the other planets.4. Its acceleration toward the Earth is zero5. None of the above

Example 13.4: The speed of the space stationA small supply satellite needs to dock with the

International Space Station (ISS). The ISS is in a near-circular orbit at a height of 420 km.

What are the speeds of the ISS and the supply satellite in this orbit?

Quiz Question 4For a satellite in a highly elliptical orbit, after it passes the

point of closest approach to the Earth (perigee) and before it reaches the point of farthest separation (apogee), its

1. potential energy will be decreasing and its kinetic energy will be increasing

2. potential energy will be increasing and its kinetic energy will be constant

3. potential energy will be constant and its kinetic energy will be decreasing

4. potential energy will be increasing and its kinetic energy will be decreasing

5. potential energy and kinetic energy will both be constant

n “Action at a distance”?

n Infinite propagation speed?

n Mercury’s perihelion precession?

Shortcomings of Newton’s Universal Law of Gravitation…

In 1915, Einstein publishes hisgeneral theory of relativity

When forced to summarize the general theory of relativity in one sentence; time and space and gravity have no separate existence from matter.

- A. Einstein

Matter tells spacehow to curve,

Space tells matterhow to move.