Newton’s laws of motion and gravityNewton’s laws of motion1. Every body continues in a state of rest or uniform motion (constantvelocity) in a straight line unless acted on by a force.(A deeper statement of this law is that momentum (mass x velocity) is aconserved quantity in our world, for unknown reasons.)This tendency to keep moving or keep still is called “inertia.”2. Acceleration (change in speed or direction) of object is proportional to:applied force F divided by the mass of the object m i.e. ⇒ a = F/m or (more usual) F = maThis law allows you to calculate the motion of an object, if you know theforce acting on it. This is how we calculate the motions of objects in physicsand astronomy.⇒ You can see that if you know the mass of something, and the forcethat is acting on it, you can calculate its rate of change of velocity, so you canfind its velocity, and hence position, as a function of time.3. To every action, there is an equal and opposite reaction, i.e. forces aremutual. A more useful equivalent statement is that interacting objectsexchange momentum through equal and opposite forces.What determines the strength of gravity?The Universal Law of Gravitation (Newton’s law of gravity):1. Every mass attracts every other mass.2. Attraction is directly proportional to the product of theirmasses.3. Attraction is inversely proportional to the square of thedistance between their centers.Newton’s Law of Gravity (cont’d):Every object attracts every other object with a force⇒ F (gravity) = (mass 1) x (mass 2) / R2 (distance squared)Notice this is an “inverse square law” (right illus.). Orbits of planets (and everything else) are a balancebetween the moving object’s tendency to move in a straightline at constant speed (Newton’s 1st law) and thegravitational pull of the other object (see below). Now we’ll see how all this can be combined to calculatethe motion of any object moving under any force (gravity orotherwise--like a magnetic force, or friction, or anything.Using Newton’s laws, continued…Applying this procedure (Newton’s 2nd law with the law of gravity) you (or atleast someone) can derive Kepler’s laws, if you know the form of thegravitational force. For gravity we have Newton’s formula Fgrav = G m1m2/dwhere G is Newton’s gravitational constant (you don’t have to know it’svalue), m1 and m2 are the two masses, and d is their separation (distancefrom each other).From this “it can be shown” that all closed orbits are ellipses, that the orbitalmotion is faster when the two objects are closer to each other (Kepler’s 2ndlaw), and Kepler’s 3rd law, the most important result.Kepler’s third law now contains a new term: P2 = a3/ (m1+ m2) Newton’s form of Kepler’s 3rd law.(Masses expressed in units of solar masses; period in years, a in AU, asbefore).⇒ This is basically what is used (in various forms) to get masses of ALLcosmic objects! Another way to word it: if you know how fast two objectsare orbiting each other, and their separation (notice you need the distanceto get this), you can solve for the sum of their masses. We will use thisover and over--it is the only way we have to get masses directly.The most important thing about Newton’s laws is that they are general: you cancalculate the motion of any object (or any number of objects) acting under anyforce can be calculated, in principle, if the force can be specified (e.g.gravitational force as a function of mass and distance; but it could be frictionalforce, magnetic force, electrostatic repulsion, ….)We calculate the evolution of clusters of stars, of millions of galaxies in anexpanding universe, of a hot gas in a magnetic field, and almost everything else,although in general this is so difficult that you can only get computer solutions.Example shown on next page.Examples: Earth’s orbital period (1 year) and average distance (1 AU) tell us the Sun’smass (think: why don’t you need to know the Earth’s mass for this purpose? Orbital period and distance of a satellite from Earth tell us Earth’s mass. Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass. This is how “black holes” were discovered to actually exist (later in course),and how the masses of planets orbiting other stars are determined. Motion of stars in galaxies reveals the existence of invisible mass, or “darkmatter,” whose nature remains unknown.A complex example of the use of Newton’s laws: Illustration below shows effect ofgravitational forces between two galaxies that are in the early stages of collisional merging.Solving Newton’s laws for millions of stars and for the gas within these galaxies, we canactually make models for such phenomena that show how tidal forces are distorting thesegalaxies. This example shows you that some orbits can decay, leading to merging of objects.We will see this again when we discuss the cannibalism of planets by their parent stars.End of material on orbits under gravity, Kepler’s laws, Newton’s lawsand the way Newton’s form of Kepler’s third law can give us themasses of astronomical objects. In fact it is just about the only way.How else can you learn about astronomical objects?All you get from them is their l i ght, so there aretwo chapters just on how we can analyze light.These are chapters 3 and 4.We will only cover chapter 3 for the first exam.Light: PropertiesProperties of Light (ch. 3 in text) This is an extremely important topic, because the only things we can learn about objectsand phenomena outside our solar system are learned by analyzing the light they send us.In a sense, astronomy is all about how to collect, analyze, and interpret light. Can consider light as waves or as particles, depending on circumstance. (One of the “bigmysteries” of physics.) Either way, it is common practice to call them “photons.” Light can be thought of as a wave that arises due to an oscillating (vibrating)electromagnetic field (see text). Unlike other kinds of waves, light does not require amaterial medium for its propagation (travel); light can propagate in a vacuum. (Don’t worry about “polarization” in text if it is confusing to you. It won’t be on the exam.)Waves: Need to understand and become familiar with the following properties of light (willdiscuss in class):Wavelength—Always denoted by Greek letter “λ”.Frequency—how many waves pass per second,
View Full Document
Unlocking...