KNOWLEDGE TO GET FROM TODAY S CLASS MEETING Class Meeting #5, Friday, January 29 th, 2016 1) GRAVITY: (text pages 111-112, 123) 2) Isaac Newton s LAWS of MOTION (briefly) (text pages 115-117) 3) Distances of interest (text pages 2, 4, 15, 70, A-15) and EARN A GOOD GRADE ON QUIZ #1
Your Lab Sections next week in Room 232 in Walden Hall will conduct the DENSITY Lab Read through the lab BEFORE your section meets!! ANY QUESTIONS? You should have a printed copy of the DENSITY Lab with you when you arrive at your Lab Section meeting The PDF of the Lab is available within the LAB-MANUAL folder at the class website: http://astronomy.nmsu.edu/murphy/astr105g-m040506- Spring2016/LAB-MANUAL/LAB02-Density-Feb03-04.pdf
QUIZ #2 WILL OCCUR: next Friday, February 5 th (the final ~20 minutes of class) Topics: i) Kepler s 3 Laws of Planet Motion ii) initial telescopic observations which supported the Sun-centered theory of Solar System structure iii) Eratosthenes determination of Earth s size iv) concepts of Mass, Volume, Density, & Gravity v) the 8 planets in our solar system and their order of increasing Orbital Semi-Major Axis value: Table E1, pg A-15 listed on the next slide are text sections and questions for quiz study
Kepler s Laws: text pgs 66-68, 70, 73,79 Text questions: Chapt 3 #s 9, 20, 25, 26, 27 Initial Observations that supported Copernicus idea: text pg 67-70 Text questions: Chapt 3 #s 723, 24, 29 Eratosthenes: text pg 63 Text questions: Chap 3 #s 45, 46 (if you can do the math, great, but the idea is what s important) Mass, Volume, Density: text pgs 113-114; 143-146 (in Chap 5) Text questions: Chap 4 #s 4, 11, 15, 26 ; Chap 5 #s 6, 7, 30 Gravity (including comparing mass to weight: text pages 123-125 Text questions: Chap 4, #s 9, 18, 19, 32, 33, 42
You should by the end of next week have read through CHAPTER 4 in the text.. and pages 143-147 in Chapt 5 (with special emphasis upon the topics we have discussed here in class PLUS Eratosthenes method for estimating Earth s circumference, and Galileo s Copernicussupporting telescope observations, both in Chapter 2)
WE LL RETURN TO THE TOPIC OF GRAVITY from our previous class but first ANY QUESTIONS????
Now, let s consider the physical process that keeps the Solar System objects (Sun, planets, moons, asteroids, comets, etc.) bound together to each other. The Force of GRAVITY which depends upon MASS
All bits of MASS (a rock, a book, a person, a helium filled balloon, a planet, a star, and individual proton or neutron or electron..) have a natural attraction for all other objects. This attraction is: GRAVITY (Section 4.4 in your text) The intensity of the attraction (GRAVITY force) between two objects depends upon two physical properties: i) the masses of the two objects ii) the distance separating the two objects
The FORCE of gravity between two objects = F GRAV = G x Mass#1 x Mass#2 / (Distance x Distance) G = 6.67 x 10-11 Newtons meters 2 / kilogram 2 (G is just a number, with units, that allows us to calculate the Gravitational force) Mass used here is in units of KILOGRAMS Distance used here is in units of METERS
In this classroom, what object is dominating the gravitational force (attraction)? -we are all attracting each other, but we are not bumping in to each other.. - pencils on tabletops are not sliding together.. - the ceiling is not pulling you out of your seat. Earth, because it is so much more massive than everything else in here, is dominating the gravity in this room, so its gravitational pull on us overwhelms our pulls on each other
The gravitational pull between the MASSes of the Earth and objects here on Earth s surface is what we know as WEIGHT We won t generally use the concept of WEIGHT during the semester for ASTR 105G BECAUSE The WEIGHT of an object is not conserved The WEIGHT of an object depends upon the GRAVITATIONAL pull upon that object: Let s compare MASS vs WEIGHT 1) You are a certain MASS (you are composed of some specific number of protons and neutrons)
2) If you go out in to space far from any planet, or star, or other object (and we ll assume that you can live this way..), you will still have the same MASS (assuming you don t lose or gain any protons or neutrons) BUT If you are very, very far from any LARGE massive.. what will your weight be? Your WEIGHT will be essentially zero because there will be essentially no GRAVITY force pulling upon you BUT Your mass will not be zero!!!
Let s calculate the intensities of several gravitational attractions 1) The Gravitational attraction (force) between YOU and the Earth is: F Grav = G Mass Earth Mass You / (Earth s radius) 2 = 6.67 x 10-11 N m 2 /kg 2 x 6 x 10 24 kg x 70 kg (6,378,000 meters) 2 = 688.66 Newtons (equivalent to 154 pounds) ------------------------------------------------------------ F Grav = Your mass times Earth s Gravity Acceleration which can be rearranged to indicate: Acceleration = F grav / Mass you
When we calculate the gravitational force between the Earth and another object, we assume that all of Earth s mass is concentrated at its center:
It is sometimes easier to think in terms of: Gravitational Acceleration = F Grav / Mass You if one mass is much, much larger than the other Earth s downward gravity acceleration at its surface: 688.66 Newtons / 70 kg = 9.8 (m/s)/s Earth s Surface Gravitaty Acceleration = 9.8 (m/s)/s Which indicates that if you, or anything else, is dropped here at the Earth s surface, its FALLING SPEED will increase by 9.8 meters per second (~20 mph) during each second that you fall
Acceleration m/s (9.8 m/s)/s Time = 0 seconds, Speed = 0 m/s (time to fall 1 meter = 0.45 seconds) Time = 1 second, Speed=9.8 m/s Distance fallen = 4.9 meters ( (= ~16.5 feet) 44.1 meters Time = 2 seconds; Speed=19.6 m/s Distance fallen=19.6 meters (= ~66 feet) Time = 3 seconds; Speed=29.4 m/s Distance fallen=44.1 meters (= ~150 feet)
What is the Gravitational Acceleration rate between two people seated side-by-side in this classroom? F Grav = G Mass Neighbor Mass You / (1 meter) 2 = 6.67 x 10-11 N m 2 /kg 2 x 70 kg x 70 kg (1) 2 = 0.000000327 Newtons (=3.27 x 10-7 Newtons) Gravitational Acceleration between you two: 3.27x10-7 Newtons / 70 kg = 5 x 10-9 (m/s)/s (equal to ~0.00000001 miles per hour per second)
SO, due to gravity: i) an object dropped from 1 meter above the ground will require 0.45 seconds to complete its fall BUT ii) Two people 1-meter apart from each other and far out in space away from any large mass (source of gravity) would require approximately 20,000 seconds (approximately 5 hrs 33 minutes) before their centers collide For Gravity Acceleration conditions: DISTANCE = ½ x Acceleration x TIME 2
So, how can these concepts be used to understand the Planets (or moons or stars)? 1) you want to know what material(s) some planet in the solar system is composed of; you can see it, and know its size (radius) (from which you can determine its VOLUME), but don t know much more. 2) if a moon orbits the object, or a spacecraft passes by, you can determine the gravitational pull of the planet upon the moon or upon the spacecraft; a measurement of the GRAVITY can then permit you to calculate the MASS of the planet
Consider a planet in the Solar System; a spacecraft is going to pass by the planet The spacecraft will feel the planet s gravitational attraction ( acceleration induced upon the craft) The magnitude of the gravitational attraction felt, and the known distance between the planet and the spacecraft, allow us to determine the planet s MASS A moon orbiting a planet can also provide information from which the planet s mass, and density can be determined
3) If you know the VOLUME of the planet and its MASS, you can determine the DENSITY of the planet: DENSITY = MASS / VOLUME 4) Planets are not pure substances, rather they are a mixture of many materials, but a planet s DENSITY can tell you if it is rocky:metallic (like Earth) or gaseous hydrogen & helium (like Jupiter), WITHOUT EVER HAVING TO GO TO THAT PLANET!!
This technique allowed astronomers to learn Jupiter s density, ~1.3 grams per cubic centimeter, well before we ever sent a spacecraft to Jupiter.. The telescopically observed apparent size of Jupiter and our knowledge of its distance from the Sun, PLUS the orbit characteristics of Jupiter s four large moons, permitted determination of Jupiter s volume, its gravitation attraction upon its moons, and thus Jupiter s mass, and.. DENSITY = MASS / VOLUME
ANY QUESTIONS ABOUT GRAVITY? ORBIT MOTIONS (planets around the Sun, the Moon around Earth, etc.) are controlled by the Gravity Force between the central object and the orbiting object Let s start to take a look at this control. with Isaac Newton s 3 Laws of Motion
Isaac NEWTON S 3 Laws of Motion (pg 115) (these help us understand orbit motions.) 1 st Law: an object continues at the same speed (which can be zero) and in the same direction unless acted upon by an outside force 2 nd Law: the acceleration (change in speed OR direction) an object experiences is directly related to the magnitude of the force applied upon the object & the mass of the object 3 rd Law: each action (force) occurs in the presence of an equal magnitude but oppositedirection action (force) [ action:reaction ].. we will next Monday discuss how gravity and Newton s laws of motion control orbit motions
Increasing Length OK, let s talk DISTANCE UNITS for a moment METRIC ENGLISH Units of length 1 centimeter (10 millimeters; 0.3937inch) 1 inch (2.54 centimeters) 1 foot(12 inches; 30.48 cm) 1 yard (3 feet; 91.44 cm) 1 meter (100 cm; 39.37 inches) 1 kilometer (1000 meters; 0.621 miles) 1 mile (1.61 kilometers) 5 kilometers (3.1 miles)
ASTRONOMICAL DISTANCES Within our Solar System, the Standard Distance is the average Sun-to-Earth distance: ~93,000,000 miles = ~9.3 x 10 7 miles [ How many kilometers is this equal to? ] 9.3 x 10 7 miles x 1.61 km per mile ~1.5 x 10 8 km (which is 391 times the Earth-to-Moon distance) This distance (150,000,000 km or 93,000,000 miles) is called: ONE ASTRONOMICAL UNIT (1 AU)!!! 1 AU Earth
In Our SOLAR SYSTEM, Planets Average Distance from the Sun range from: Closest to the Sun MERCURY: 0.387 AU (= 6 x 10 7 km = 37 million miles) to Farthest from the Sun PLUTO: 39.48 AU (= 6 x 10 9 km = 3.7 billion miles) (and remember, Earth is 1 AU from the Sun)
While AUs are a very nice length scale to employ when talking about distances within our Solar System (better than meters, or feet, or leagues) AU s are not very useful when discussing distances BETWEEN stars within our Milky Way Galaxy FOR EXAMPLE: The Sun s nearest stellar neighbor, a star named ALPHA CENTAURI, is located: ~250,000 AU (= 2.5 x 10 5 AU) from the Sun What other Astronomical unit(s) are you familiar with?
PARSEC= 3.1 x 10 13 kilometers (=210,000 AU) LIGHT YEAR= 9.5 x 10 12 km (= 63,000 AU) (so. 1 PARSEC = 3.3 LIGHT YEARS) What does a LIGHT YEAR really mean? ( is it a time duration, or a distance, or.? ) A TIME = DISTANCE EXAMPLE: How far is it from Las Cruces to Deming? 97 kilometers (60 miles) -------------------------------------------------------- But, what if I said, It is one hour to Deming. How would you interpret this?
Travelling at freeway speed, on I-10, a time interval of one hour will get me to Deming --------------------------------------------------------- So, a time interval at a known speed = a distance This is the idea behind the distance unit of a LIGHT YEAR ONE LIGHT YEAR = the distance light travels in one year = SPEED OF LIGHT times a time interval of 1 YEAR = 3 x 10 8 meters per second x 365.25 days per year x 86,400 seconds per day = 9.5 x 10 15 meters (= 9.5 x 10 12 km = 5.9 x 10 12 miles)
ONE LIGHT YEAR = ~ 63,000 AU Speed of light = 186,000 miles per second = 3 x 10 8 meters per second How far apart are the Sun and Earth? 1 AU = 1.5 x 10 8 kilometers = 93,000,000 miles How about their distance in LIGHT TIME? ~8 minutes! So, sunlight striking the Earth s surface here in Las Cruces right now left the Sun 8 minutes ago
Since the Speed of Light is the fastest speed physics allows, if the Sun was to shut off right now, we would not know about it for ~8 minutes Mercury (0.4 AU) is 3.2 light minutes from the Sun, Pluto (40 AU) 320 minutes or 5.33 hours from the Sun ANY QUESTIONS ABOUT GRAVITY, or DISTANCES?