Astronomy 101Introduction to AstronomyWinter 2010Part 1: Labs 1-7Credits:Cover image of M51 from NASA’s Hubble Heritage Project - Labs: Gravity:Oliver Fraser, Julianne Dalcanton - Atoms: Apocryphal, Julianne Dalcanton -Thermal Radiation: Julianne Dalcanton - Atoms & Light: Apocryphal, Julianne Dalcan-ton - Spectral Classification of Stars: Stacey Palen, Richard Plotkin, Julianne DalcantonColors: Julianne Dalcanton - Color-Magnitude Diagrams: Marcel Agueros, Nate Mc-Crady, Ana Larson, Julianne Dalcanton - Measuring Distance: Todd Grinsteiner, JulianneDalcanton - Galaxy Classification: Andrew West, Julianne Dalcanton - Dark Matter:Greg Stinson, Julianne Dalcanton - Hubble Law: Luis Mendoza, Toby Smith, Ana Lar-son, Julianne Dalcantonc° 2010 Julianne Dalcanton - unless otherwise credited the images are copyrighted byNASA, the Sloan Digital Sky Survey, or by the author. Permission is given to make anddistribute copies of this document for educational purposes.Lab #1 GravityIntroduction to GravityGravity is one of the most important forces in astronomy. Unlike the “strong” and the“weak” forces, it can act over the very long distances that are characterstic of Space1.For this course, you will need to learn a few simple facts about gravity and how it works.1. Gravity is always “attractive”, meaning it can only pull objects towards each other.2. The gravitational force between two objects depends on only two things:• How massive the two objects are• How far apart the two objects are3. The gravitational force attracting two objects together increases if the mass of eitherobject increases.4. The gravitational force attracting two objects together increases if the objects arecloser together.5. The formula describing the strength of the gravitational force between two objects withmasses M1and M2, separated by a distance D isFGravity= GM1M2D2G is a constant which describes how strong the force of gravity is. It is known as“Newton’s Constant” and has a value of G = 6.67×10−11meters3/(kilogram×seconds2).6. The separation D between two objects is defined as the separation between their cen-ters, not their edges. For example, if you calculate the gravitational force between twoadjacent soccer balls that were touching each other, the separation would be about 22cm, rather than zero.7. The equation describing the force of gravity shows that• The force increases linearly with the mass of either object (i.e. if you doublethe mass of one object, the force between the objects doubles as well)• The force decreases as the square of the separation (i.e. if you double theseparation between the objects, the force decreases by a factor of 4 (= 22)).1The electromagnetic force can also act over long distances. However, since the universe is electricallyneutral (i.e. there is no postively charged galaxy attracting some other negatively charged galaxy), electricalforces play a role only on very small scales.Astronomy 101 1 – 1 Introduction to Astronomy8. Sometimes (such as later in this lab), you are not interested in exactly how big agravitational force is in absolute terms, but are instead only interested in how big it iscompared to some other force. For example, suppose you wanted to compare the forceof gravity that the Earth feels from the Sun to the force that the Earth feels from theMoon. The force that the Earth feels from each object is:FGravity,Sun= GMSunMEarth(DSun)2FGravity,Moon= GMMoonMEarth(DMoon)2where DSunand DMoonare distances measured from the center of the Earth to thecenter of the Sun and Moon, respectively. Dividing the force due to the Sun by theforce due to the Moon gives the ratio of the two forces. A bit of simple algebra thenshows that:FGravity,SunFGravity,Moon=MSunMEarth(DSun)2÷MMoonMEarth(DMoon)2=µMSunMMoon¶µDMoonDSun¶2Therefore, for two objects, the ratios of their masses and their distances are sufficientto tell you which object produces the stronger gravitational force, and by how much.9. Gravitational force has the units of mass times acceleration. Acceleration is therate at which velocity changes, and thus has units of (meters/second)/second, ormeters×seconds−2. Force therefore has units of kilograms×meters×seconds−2. Thiscombination of units is sometimes called “a Newton”, after Sir Isaac Newton. OneNewton of force can accelerate a 1 kilogram mass by 1 meter per second every second.QuestionsUsing the information above, please answer the questions on the on-line quiz before section.Then, continue on to the questions in the remainder of this lab, and turn in the completedlab to your TA.Astronomy 101 1 – 2 Introduction to Astronomy3. In this question, you will use your knowledge of gravitational forces to decide whetheryou feel more force from your friend standing 3 meters away from you, the planet Jupiter,or the nearest spiral galaxy, Andromeda (M31). It is not obvious what the answer will be,since Jupiter and Andromeda are much more massive, but also much further away!a) The following table constains data on the distances and masses to the objects you’ll beconsidering. Estimate the mass of your best friend, and fill in your answer in the followingtable. Please use kilograms. For those of you who are not metricly inclined, 1 kilogram isroughly equal to 2.2 pounds. Please write your answer in scientific notation!Your Friend Jupiter AndromedaMass(kilograms)2 × 1027kg 1 × 1042kgDistance FromYou (meters)3 m 7 × 1011m 1 × 1022mb) Using the data in the table above, calculate the ratio between the masses of Jupiter andyour friend, and between Andromeda and Jupiter. Fill in your answers in scientific notationin the table below.c) Repeat part (b) using the distances.d) Using your answers for (b) and (c), calculate the ratio between the gravitational forces.Record your answers in the table. Do not calculate the actual force on you in Newtons, sinceyou can derive the ratio of forces just from knowing the ratios of distances and of masses!JupiterYourFriendAndromedaJupiterRatio of MassesRatio of DistancesRatio of GravitationalForcese) You feel more force from [Your Friend/Jupiter].f) You feel more force from[Jupiter/Andromeda].Astronomy 101 1 – 3 Introduction to Astronomy4a) How close would you have to stand for the gravitational pull from your friend to be asstrong as the gravitational pull of Jupiter? Please show your reasoning and circle your finalanswer. Make sure to use units!b) Would you be comfortable being this close to a
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