Astronomy 1020-HSpring_2015

Day-9Stellar Astronomy

Course Announcements• Smartworks Chapter 2: Start on –

Grades will be downloaded sometime this coming weekend.

• SW Chapter 3 … will be downloaded on Friday 2/13 during the exam.

• SW Chapters 13-23 are posted now• Exam 1: Friday, Feb. 13• 1st set of Dark Sky observing nights:

• Wed. Feb. 11 & Tues. Feb. 17

Lab This Week• Hydrogen Energy Levels

• What you need to know:• You get to explore the possible energy

transitions for Hydrogen.• Reading ahead in Chapter 5 will help.

Tutorial: Newton’s Law and Gravity – pg.29

Work with a partnerRead the instructions and questions carefullyTalk to each other and discuss your answers

with each anotherCome to a consensus answer you both agree

onIf you get stuck or are not sure of your

answer ask another groupIf you get really stuck or don’t understand

what the Lecture Tutorial is asking as one of us for help

Concept Quiz—Earth’s Position

Assume Earth were moved to a distance from the Sun twice that of what it is now. How would that change the gravitational force it would experience from the Sun?

A. It would be half as strong.

B. It would be one-fourth as strong.

C. It would be twice as strong.

D. It would be four times as strong.

E. It would not change.

The gravitational acceleration at the surface of Earth, g, can be solved for by using the formula for the gravitational force and Newton’s second law.

The m cancels. g is the same for all

objects at the same R.

MATH TOOLS 4.1MATH TOOLS 4.1

Newton’s Law of Gravitation• Newton’s law of gravitation states: Two bodies attract each other

with a force that is directly proportional the product of their masses and is inversely proportional to the square of the distance between them.

gmF

m

mkgkgNm

F

d

mGmF

grav

object

grav

grav

26

242

211

1038.6

1097.51067.6

2

21

g ~ 10 m/s2 “the acceleration of gravity” & g x m is your weight!

Concept Quiz—Gravity and Weight

Your weight equals the force between you and Earth.Suppose you weigh 600 newtons. The force you exert on

Earth is:

A. 600 newtons.

B. much smaller than 600 newtons because your mass is much less than Earth’s.

C. exactly zero, since only massive objects have gravity.

Concept Quiz—Earth and Moon

Earth and the Moon have a gravitational force between them. The mass of the Moon is 1.2 percent of that of the Earth. Which statement is incorrect?

A. The force on the Moon is much larger than that on Earth.

B. The forces are equal size, even though the masses are different.

C. The Moon has a larger acceleration than Earth.

Gravity works on every part of every body. Therefore, self-gravity exists within a planet. This produces internal forces, which hold the

planet together.

CONNECTIONS 4.1CONNECTIONS 4.1

There’s a special case: spherically symmetric bodies.

Force from a spherically symmetric body is the same as from a point mass at the center.

CONNECTIONS 4.1CONNECTIONS 4.1

The velocity of an object traveling in a circular orbit can be found by equating the gravitational force and the resulting centripetal force.

This yields: You can solve for the period by noting that

This yields Kepler’s third law:

MATH TOOLS 4.2MATH TOOLS 4.2

In order to leave a planet’s surface, an object must achieve a velocity greater than the planet’s escape velocity.

Therefore, Earth’s escape velocity is

MATH TOOLS 4.3MATH TOOLS 4.3

Newton derived Kepler’s laws from his law of gravity.

Physical laws explain Kepler’s empirical results:

Distant planets orbit more slowly; the harmonic law and the law of equal areas result.

Newton’s laws were tested by Kepler’s observations.

The gravitational interaction of three bodies leads to Lagrangian equilibrium points.

These are special orbital resonances where the object at that point orbits in lockstep.

SOHO is near L1.

CONNECTIONS 4.2CONNECTIONS 4.2