Newton’s laws of motion and gravity1. 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.” (Nobody reallyknows what it means.)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 youcan find 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:1. Every mass attracts every other mass.2. Attraction is directly proportional to the product of their masses.3. Attraction is inversely proportional to the square of the distancebetween their centers.Newton’s Law of Gravity: 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”(left illus. below). Orbits of planets (and everything else) are a balance between the moving object’s tendency tomove in a straight line at constant speed (Newton’s 1st law) and the gravitational pull of the otherobject (right illus.). Now we’ll see how all this can be combined to calculate the motion of anyobject moving under any force (gravity or otherwise--like a magnetic force, or friction, or anything.More on the Newton’s law of gravity How is this “force” transmitted instantaneously, at a distance? (“Gravitons”--translation: we don’t know). Today, gravity interpreted as a “field” that is aproperty of space-time itself, or even stranger interpretations… But for almost all applications, Newton’s law of gravity is sufficient for usto calculate the orbits of nearly all astronomical objects. We only need tocombine it with Newton’s 2nd law (a = F/m, where F is the expression for theforce of gravity); then we can solve for the acceleration, which is the change ofvelocity with time. This gives us the velocity (you have to solve a “differentialequation” a = dv/dt = …) and position of the object as a function of time. From this you (or at least someone) can derive Kepler’s laws from Newton’slaws of motion and the form of the gravitational force. The result for Kepler’sthird law 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, as before). This is basically what is used (in various forms) to get masses of ALL cosmicobjects! Another way to word it: if you know how fast two objects are orbitingeach other, and their separation (notice you need the distance to get this), youcan solve for the sum of their masses.But the most important application is that the motionof any object (or number of objects) acting under anyforce can be calculated, in principle, if the force canbe specified (e.g. gravitational force as a function ofmass and distance)Examples:• Earth’s orbital period (1 year) and average distance (1AU) tell us the Sun’s mass.• Orbital period and distance of a satellite from Earth tellus Earth’s mass.• Orbital period and distance of a moon of Jupiter tell usJupiter’s mass.● Motion of stars in galaxies reveals the existence ofinvisible mass, or “dark matter,” whose nature remainsunknown.Illustration below shows effect of gravitational forcesbetween two galaxies that are in the early stages of merging.Solving Newton’s laws for millions of stars and for the gas withinthese galaxies, we can actually make models for such phenomenathat show what is going on (tidal forces in this case). This exampleshows you that some orbits can decay, leading to merging of objects.We will see this again when we discuss the cannibalism of planets bytheir parent stars.New topic: Properties of Light (ch. 3 in text) This is an extremely important topic, because the only thing we can learn about things outsideour solar system is by analyzing the light they send us. In a sense astronomy is all about how tocollect, 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) electromagneticfield (see text). Unlike other kinds of waves, light does not require a material medium for itspropagation (travel); light can propagate in a vacuum. (Don’t worry about “polarization” in text if it is confusing to you.)Waves: Need to understand and become familiar with the following properties of light (will discussin class):Wavelength—Always denoted by Greek letter “λ”.Frequency—how many waves pass per second, denoted “f”Speed—All light waves travel at the same speed, the “speed of light”, “c”(=3x105km/sec = 2.86x105 mi/sec (286,000 miles per second); no need to memorize these numbers!) Energy--the energy of a photon is its frequency times its speed E = f x cIt is extremely important that students become familiar and comfortable with these terms andsymbols--they will recur throughout the class.The fact that light travels at a finite speed (“c”) means that we seedistant objects as they were in the past. Consider our neighbor, theAndromeda galaxy shown in Fig. 3.1 in your text—it is about 2 millionlight years away… Later we will “look back” to times near thebeginning of the universe (billions of years ago) using very distantgalaxies. Spectrum: Possibly the most important term to understand inthis course! It refers to the mixture of light of different wavelengthsfrom a given source; best to remember it as a graph of “intensity” (orbrightness) of radiation in each wavelength (or frequency)
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