ch14_kmlv


 * Chapter 14: Satellite Moon **

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14.1 Earth Satellites ·  An earth __**satellite**__ is a projectile that falls around the earth rather than into it. · Anything dropped form rest on earth accelerates at a rate of 10 m/s² and falls a vertical distance of 5m in the 1st second (More precise measurements are 9.8 m/s² and 4.9 m). · The earth’s curvature of the surface drops a vertical distance of 5m for every 8000m tangent to its surface o Ex: If you were swimming in a calm ocean, you would be able to see only the very top of a 5m-tall mast on a ship that is 8 km away. · Orbital speed for close orbit about the earth is 8 km/s (29000 km/h or 18000 mi/h). · Because of atmospheric friction that would burn everything up, satellites stay at about 150 km or more above the earth’s surface.  "The earth curves down 5 m every 8000 m (5 mi) traveled along its surface." []

 "One meter = 3.28 ft One mile = 5280 ft One hour = 3600 sec If the rock is thrown with a speed of 8000 m/s (26000 ft/s = 5 miles/s) it will orbit the earth. 5 miles/s = 18,000 miles/hr." []

14.2 Circular Orbits  []

> · A satellite is always moving perpendicular to the force of gravity so it doesn’t move in the direction of gravity, which would increase its speed, nor does it move in a direction against gravity, which would decrease its speed, so it exactly “criss-crosses” gravity. > · The time it takes for a satellite to make one complete orbit is a period (a satellite close to earth has a period of 90 minutes). > <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· A special kind of circular orbit is a geosynchronous or geostationary orbit. > <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Geosynchronous/Geostationary orbit- An orbit over the equator with a period of 24 hours and will cause the satellite to always be above the same point on earth (used for communications satellite). <span style="font-size: 120%; font-family: Impact, Charcoal, sans-serif;"> " The moon's forward velocity, v, allows it to maintain the same distance, even though it's constantly being pulled toward the earth." <span style="font-size: 70%; font-family: Impact, Charcoal, sans-serif;">[]
 * <span style="font-size: 120%; color: #800080; font-family: Impact, Charcoal, sans-serif;"> In a __**circular orbit**__ the speed of a circling satellite is not changed by gravity.

<span style="display: block; font-size: 200%; color: #0000ff; font-family: 'Lucida Console', Monaco, monospace; text-align: center;">14.3 Elliptical Orbits <span style="font-size: 120%; color: #ff9900; font-family: Impact, Charcoal, sans-serif;"><span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· An **__ellipse__** is created by a projectile just above the atmosphere at a horizontal speed somewhat more than 8 km/s that overshoots a circular path and traces an oval-shaped path. <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· An **__ellipse__** is the closed path taken by a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant. <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· The speed of the Satellite will be smallest at the highest point (called the apogee) and largest at the lowest point (called the perigee).

"The sun is one of the foci of the elliptical orbits of the planets." []

"Two tacks represent the two different foci of the ellipse." []

<span style="display: block; font-size: 200%; color: #0000ff; font-family: 'Lucida Console', Monaco, monospace; text-align: center;">14.4 Energy Conservation and Satellite Motion <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· The total energy (kinetic plus potential) of any satellite is constant <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· In an elliptical orbit one kind of energy is constantly being traded for the other <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· In a circular orbit, both kinetic and potential energy remain constant <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Energy in both elliptical and circular orbits always add up the same

"When the satellite is closest to the Earth, its speed is greatest." []

<span style="display: block; font-size: 200%; color: #0000ff; font-family: 'Lucida Console', Monaco, monospace; text-align: center;">14.5 Escape Speed <span style="font-size: 120%; color: #29db72; font-family: Impact, Charcoal, sans-serif;"><span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· The **__escape speed__** of an object is the speed that something must travel to completely lave earth (or another planet or star). <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· The escape speed of an object on the earth’s surface is 11.2 km/s. <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Anything launched slower than 11.2 km/s will eventually return to earth and anything faster will not. <span style="font-family: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol; msofareastfontfamily: Symbol; msobidifontfamily: Symbol; msolist: Ignore;">· Escape speed is reduced when the object starts from farther away or if the planet has a smaller mass.

"For a near-earth orbiting satellite, rocket reaches desired altitude, and turns right, reaching orbital speed." []

<span style="display: block; font-size: 200%; color: #0000ff; font-family: 'Lucida Console', Monaco, monospace; text-align: center;">Escape Speeds: <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">Review: \displaystyle V_e_s_c_a_p_e=\sqrt{\displaystyle(\frac{20m}{d})} math \displaystyle d= {(\frac {1}{2})}at^2 = {(\frac {1}{2})(9.8{(\frac {m}{s})})(1s)^2 = 4.9m math > The horizontal and vertical motion are independent of each other, the ball will fall 4.9m in each case. \displaystyle V= {(\frac {2\pi}{T})} = {(\frac {(2\pi)(1.5 x 10^{11}m)} {365 x 24 x 3600})} = 3 x 10^4 {(\frac {m}{s})} math \displaystyle V= {(\frac {2\pi}{T})} = {(\frac {(2\pi)(3.85 x 10^{8}m)} {27.3 x 24 x 3600})} = 1030 {(\frac {m}{s})} math \displaystyle V_e_s_c_a_p_e=\sqrt{\displaystyle(\frac{20m}{d})}= \sqrt{(\frac{20(6.673 x 10^ {-11} (\frac {N x m^2} {kg^2}) {(\frac {7.35 x 10^{22} kg})}} {(1.74 x 10^6 m)}} = 2400 {(\frac {m}{s})} math > > > > > > > Source: Hewitt, Paul G., __Conceptual Physics.__ Menlo Park, California: Addison Wesley Longman, Inc., 1999. >
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Astronomical Body** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Mass (Earth)** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Radius (Earth)** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Escape Speed (Km/s)** ||
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Sun** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**333,000** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**109** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**620** ||
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Saturn** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**95.2** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**9.2** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**36.0** ||
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Earth** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**1.00** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**1.0** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**11.2** ||
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Mars** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**0.11** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**0.53** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**5.0** ||
 * = <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**Moon** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**0.0123** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**0.27** ||= <span style="display: block; font-size: 120%; color: #bf22bf; font-family: Tahoma, Geneva, sans-serif; text-align: center;">**2.4** ||
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**Terms**:
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Apogee__**- The point in a satellite's elliptical orbit farthest from the center of the earth.
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Focus__**- For an ellipse, on of the two points for which the sum of the distances to any point on the ellipse is a constant. A satellite orbiting the earth moves in an ellipse that has the earth at one focus.
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Ellipse__**- An oval-shaped curve that is the path of a point that moves such that the sum of its distances from two fixed points (foci) is constant.
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Perigee__**- The point in a satellite's elliptical orbit where it is nearest to the center of the earth.
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Escape Speed__**- The minimum speed necessary for an object to escape permanently from a gravitational field that holds it.
 * <span style="color: #00bcff; font-family: Arial, Helvetica, sans-serif;">**__Period__**- The time required for a complete orbit.
 * **Questions**:
 * 1) If we drop a ball from rest, how far will it fall vertically in the first second? If we instead move our hand horizontally and drop it (throw it), how far will it fall vertically in the first second?
 * 2) What do the distances 8000m and 5m have to do with a line tangent to the earth's surface?
 * 3) Why doesn't gravitational force change the speed of a satellite in a circular orbit?
 * 4) Does the period of a satellite increase or decrease as its distance from the earth increases?
 * 5) Why does gravitational force change the speed of a satellite in an elliptical orbit?
 * 6) a) Where in an elliptical orbit is the spped of a satellite maximum? b) Where is it minimum
 * 7) The sum for PE and KE for a satellite in a circular orbit is constant. Is the sum also constant for a satellite in an elliptical orbit?
 * 8) A satellite can orbit at 5km above the moon, but not at 5km above the earth. Why?
 * 9) Does the speed of a satellite around the earth depend on its mass? Its distance from earth? The mass of the earth?
 * 10) If you stopped an earth satellite dead in its tracks, it would simply crash to earth. Why, then, does the communications satellites that "hover motionless" above the same spot on the earth not crash into earth?
 * 11) When does a satellite in an elliptical orbit reach maximum gravitational force; speed; velocity; momentum; KE; gravitational PE; total energy; angular momentum; acceleration?
 * 12) Calculate the speed at which the earth revolves around the sun in m/s. NOTE: The orbit is nearly circular.
 * 13) Calculate the speed at which the moon revolves around the earth in m/s. NOTE: The orbit is nearly circular.
 * 14) Escape speed at a distance d from the center of a body of mass M is:
 * math
 * **Answers**:
 * 1) math
 * 1) The earth's surface curves away 5m for every 8000m of horizontal distance.
 * 2) There's no force component in the direction of motion for a satellite in a circular orbit.
 * 3) The farther from the earth a satellite, the longer its period.
 * 4) There is a component of the gravitational force in the direction of motion, which causes an acceleration in that direction.
 * 5) a) The speed of a satellite is greatest when it is at the lowest point (the perigee). b) The speed of a satellite is least when it is at the highest point (the apogee).
 * 6) The sum of PE and KE is always constant for any satellite regardless of the type of orbit.
 * 7) There is too much air resistance at 5km of altitude above the earth, so the satellite would slow down and fall to earth.
 * 8) The speed of a satellite around the earth is independent of the mass of the satellite but it does depend on both the distance from earth and the mass of the earth.
 * 9) They don't crash into the earth because they are in a geostationary orbit and are orbiting the earth at a high speed so they appear to be motionless relative to the earth because the earth is also rotating underneath them.
 * 10) The maximum gravitational force, speed, velocity, momentum, and acceleration occur when the satellite is closest to the object it is orbiting. The maximum gravitational PE occurs when the satellite is farthest away from the object it is orbiting. However, total energy and angular momentum are both constant.
 * 11) math
 * 1) math
 * 1) math