Note it they ancients had known Newton s first law, the retrograde motion of the planets would have told them that the Earth was moving.

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1 6/24 Discussion of the first law. The first law appears to be contained within the second and it is. Why state it? Newton s laws are not always valid they are not valid in, say, an accelerating automobile. We use Newton s first law to tell if we are in a proper frame of reference. Note it they ancients had known Newton s first law, the retrograde motion of the planets would have told them that the Earth was moving. Discussion of the second law. It does four things: 1. It operationally defines force; that is, it gives a method that, in principle, force can be measured. 2. It operationally defines mass. Apply a known force to a body, measure its acceleration, and the ratio of force to acceleration gives the mass. 3. Given a desired path for a body to follow, it allows us to calculate the forces needed to produce that path. 4. Given the forces on a body, it allows us to calculate the path of the body. Note: If we are in an accelerated frame of reference in which Newton s laws are not valid, we can still use Newton s second law with the introduction of fictitious forces artifacts of the motion of the reference frame. The centrifugal force is a fictitious force in a rotating frame of reference. Discussion of the third law. Note that if the action is the force of A on B, then the reaction is the force of B on A. The third law holds even in accelerated frames of reference. Unit of force: US Customary Unit pound or lb The SI unit of force is the newton = N. If we use Newton s second law F = ma. 1 N = (1kg)(1m/s 2 ) = 1 kg m/s 2 Note that 1 N is roughly 1/5 of a lb.

2 Newton s Law of Gravity: The gravitational force between two spherical bodies is proportional to the product of their masses and inversely proportional to the square of the distance between their centers: where G = N m 2 /kg 2. We can use Newton s Law of Gravity to explain the tides: The tides are caused by the gravity of the Moon and the Sun concentrate on the Moon. Without the Moon or Sun, the water would be evenly distributed around the Earth (we are ignoring the presence of land masses). Because the Moon s gravity gets weaker with distance, it pulls harder on the water on the near side of the Earth than it does on the Earth pulls water away from the Earth forming a tidal bulge. By the same token, the Moon s gravity pulls harder on the Earth than it does on the water on the far side of the Earth. It pulls the Earth away from the water forming a second tidal bulge. The Earth rotates below the water forming two high tides and two low tides each day. The Sun tides have about half the size of the Moon tides. The tides are largest at new Moon and full Moon. The tides are smallest when Sun, Earth, and Moon form at 90 degrees. Of greatest importance, Newton, using his laws of motion coupled with his law of gravity, was able to derive Kepler s three laws of planetary motion. Most importantly of all, he was able to show that the constant of proportionality in Kepler s third law depended on the masses of the bodies in orbit about one another. If we agree to measure masses in units of the mass of the Sun, we can write Kepler s third law, as modified by Newton, in the following way:

3 Here M 1 and M 2 are the masses of the bodies in orbit about one another. If, as is the case in the solar system, we can ignore the small mass of the planet, we can write where M is the mass of the body orbited about in units of the mass of the Sun. Note: the mass of the Sun is kg. Note: Kepler s third law as modified by Newton is used to measure the masses of astronomical bodies. Example: Use the orbital parameters of the Moon to calculate the mass of the Earth. Difference between Weight and Mass Weight The weight of a body is the force of gravity on the body. From this definition and Newton s second law, we can find a mathematical expression for the weight of a body. Force is mass times acceleration: F = ma. A body in free fall has a constant acceleration due to gravity = g = 9.8 m/s 2. The force on a body in free fall is just its weight w. Thus, the weight of the body is given by w = mg. Weight has a direction downward. The weight of a body depends on where it is because g changes from place to place. Mass: The mass of a body is a characteristic of the body. The mass of a body is a measure of how hard it is to change the motion of a body called inertia. Mass doesn t have a direction associated with it.

4 Being a characteristic of a body, it does not change from place to place. Chapter 3 Light and Telescopes Properties of Light: For the most part, we will treat light as a wave. The tops of the hills are called crests; the bottoms of the valleys are called troughs. The amplitude A of a wave is half the vertical distance between a crest and a trough The brightness or intensity of the light is proportional to the square of the amplitude. The wavelength of a wave is the distance between adjacent crests. The period P of a wave is the time it takes for one crest to be replaced by the next in line start a stopwatch when the first crest passes and stop it when the next crest passes to measure the period. The frequency of a wave is the rate at which crests pass a point in space it is the reciprocal of the period: Unit of frequency = hertz = Hz (old unit, cycle per second). Important relation between the frequency, wavelength and speed of a wave. Since we will mostly be talking about light, we will use c, the symbol for the speed of light, for speed. Speed is defined to be the distance traveled divided by the time to travel the distance. Note that a wave moves a distance equal to one wavelength in a time equal to one period:

5 Since the frequency is the reciprocal of the period, we can write this as Example: Most efficient length of telescoping FM antenna. Radio station is Alice 97.3! Need to know: The frequency of the radio station in MHz is the number tuned to: 97.3 MHz. Most efficient length of antenna is 1/4 of a wavelength. Use the relation between wavelength, frequency, and speed of a wave to find the wavelength of the radio signal from the Alice. Electromagnetic Spectrum in terms of wavelength Radio Waves 10 cm and up Microwaves 10 cm down to 1 mm Infrared 1 mm down to 700 nm Visible 700 nm to 400 nm Ultraviolet 400 nm down to 10 nm X rays 10 nm 0.01 nm Gamma rays 0.01 nm and down Only two parts called windows of the electromagnetic spectrum get through the atmosphere: radio waves and visible. Telecopes: Two main types: refracting and reflecting. Refracting Telescope: Made completely of lenses. Astronomical telescopes use converging lenses. A converging lens takes light parallel to the axis of the lens and focuses it at a point called the focal point.

6 In a telescope, light comes in from very far away and is essentially composed of parallel rays. The lens through which the light enters the telescope is called the objective lens it forms an image of the object viewed around the focal point of the lens. We use the eyepiece or ocular as a magnifying glass to view the image produced by the objective. In the figure, the red rays come from the center of the arrow, which is the object. It is focused at the center of the image, which is the upside down arrow inside the telescope. The rays just above the red ones come from the tip of the arrow and are focused at the tip of the image arrow inside the telescope. The rays below the red ones come from the base of the arrow and are focused at the base of the image arrow inside the telescope. The eyepiece uses this image arrow as an object, and acting as a magnifying glass, produces the pink arrow image. The angle subtended by the pink image is larger than that subtended by the original object arrow, which means that it will appear bigger to the eye. Note, too, that the final image is upside down. The magnification of a telescope is the ratio of the focal length (distance between the lens and its focal point) of the objective to the focal length of the ocular: Reflecting Telescope: Uses a mirror for the objective but still uses a lens for the ocular. Rays of light parallel to the axis of a mirror are reflected through the focal point of the mirror. In a reflecting telescope, the mirror forms the image of the distant object around its focal point.

7 The light must redirected so that the observer will not block the light from getting into the telescope. Two main types of reflectors: Newtonian deflects the light out the side of the scope. Cassegrain reflector cut a hole in the objective mirror (where not light reaches anyway) and put a mirror in the scope to reflect the light through the hole. Professional Considerations All stars even with the largest telescopes show images as points of light. To analyze light from stars, need as much light as possible astronomers want maximum light-gathering power. More light-gathering power if the opening or aperture of the telescope is larger. Resolving Power the ability to see to closely separated objects as two objects important for analyzing binary star systems. We also improve resolving power by making telescopes larger. There is a limit to how large refracting telescopes can be made objective lens, supported around its edges, will sag over time and destroy the optics. No sagging problems with a mirror supported everywhere underneath. Even mirrors have a limit as to size use segmented mirrors or two or more large telescopes that work in concert. Also concerned about the atmosphere three ways to deal with the atmosphere: 1. Put telescope into space Hubble Space Telescope. 2. Combine signals from two or more telescopes the turbulence will be different for the different scopes computer removes everything from the signals not the same among the signals. 3. Adaptive Optics turbulence in the atmosphere is analyzed by sending a laser beam into the atmosphere and analyze the reflections. Then the computers change the shape of the secondary mirror in Cassegrain telescope to correct for the turbulence.

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