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Clark's Dream ​Exploration Series ​ ​www.ck12.org CLARKE’S DREAM ------- ​ ​Interactive Physics Simulation ​ ​------- Page 01 ​Exploration Series ​ ​www.ck12.org Which is the best orbit for a communications satellite? Sir Arthur Charles Clarke was an inventor and science fiction writer, perhaps most famous for writing ​2001: A Space Odyssey.​ In 1945, Arthur C. Clarke proposed that communications satellites be placed in “geosynchronous” orbit around the Earth. A satellite in geosynchronous orbit takes 24 hours to orbit the Earth. This means, seen from the turning Earth, it appears to stand still. Fixed satellite dishes - like the ones you might see decorating homes for satellite television - are aimed at satellites in geosynchronous orbit. Let's understand the physics behind this.The Earth takes 24 hours to rotate on its axis - we've sped that up to 24 seconds. Near-Earth satellites take 1.5 hours to orbit the Earth - here, they whiz around every 1.5 seconds. Objects in more distant orbits feel a weaker acceleration due to the Earth's gravity, and so orbit more slowly. At a very precise distance, the orbital period of the satellite matches that of Earth. To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 02 ​Exploration Series ​ ​www.ck12.org Radius of orbit - T​ his slider allows you to adjust the orbital radius of the satellite. Your task is to find the radius at which the orbital PERIOD of the satellite is exactly 24 hours. With this period, the satellite will appear “fixed” in the sky as seen from Earth, since it is rotating with the Earth. Acceleration due to gravity vs orbital radius - ​A common misconception is a belief that gravity “disappears” in space. In fact, the Earth's gravity extends to great distance. The acceleration due to gravity is approximately 9.8 2 m/s​ ​ at the Earth's surface. As you move outward, this value falls with the square of your distance from the center of the planet. Gravity gets weaker with distance. Orbital period in hours vs orbital radius - ​A satellite in circular orbit takes longer to orbit if it is farther from the Earth. This graph demonstrates the relationship between orbital size and period. To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 03 ​Exploration Series ​ ​www.ck12.org Adjust the Radius of Orbit so that the Acceleration due to Gravity is at its minimum. (​ Maximize the Radius of Orbit slider to minimize the Acceleration due to Gravity). At what Radius of Orbit will a spacecraft take 18 hours to orbit once around the Earth? ​(Adjust the Radius of Orbit slider until the spacecraft has an orbital time period of 18 hours). At what distance from the Earth will a spacecraft have to orbit to have a period of 24 hours (commonly referred to as a geosynchronous orbit)? ​(Adjust the Radius of Orbit slider until the spacecraft has an orbital time period of 24 hours). To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 04 ​Exploration Series ​ ​www.ck12.org Challenge ME! If the Earth had a lower mass, would the distance to geosynchronous orbit be higher or lower? Does the distance to geosynchronous orbit depend on the mass of the satellite in question? Why or why not? Why do you think it is (in general) less expensive to launch satellites with 90 minute orbits than 24 hour orbits? Need Help? Check out the AC Transformer Walkthrough video at:​ https://youtu.be/ALapgWB6ZOg To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 05 ​Exploration Series ​ ​www.ck12.org Are there many satellites in geosynchronous orbit? There are dozens and dozens of them - commercial and classified military communication and Earth-observation satellites abound in geosynchronous orbit. A list can be found here: http://en.wikipedia.org/wiki/List_of_satellites_in_geosynchronous_orbit Are there other interesting orbital locations? Yes, many. Of interest to astronomers in recent years is the 2nd Lagrange point, also known as L2. Orbits at L2 are solar orbits that keep the Earth directly in front of the Sun from the perspective of the satellite. The combined gravitational attractions from the Earth and Sun allow the orbit to have greater radius than the radius of the Earth, but orbit with the same period as the Earth. Tell me more about Arthur C. Clarke! One of the most important figures in science fiction, Arthur C. Clarke wrote such classics as 2001: A Space Odyssey and Rendezvous with Rama. He lived the last five decades of his life in Sri Lanka, where his adventures in scuba diving led him to discover the famous ruins of an ancient temple. How do the satellites communicate with Earth? The satellites use radio signals, which are long wavelength light waves that require very little power to generate. The Earth's atmosphere is transparent to most radio waves, just as it is transparent to visible light. Although in early years the signal would be communicated through variations in amplitude or frequency of the radio signal (AM - amplitude modulation / FM - frequency modulation), now the signals are digital in nature. This means that, something like with the old Morse Code, they flash on and off rapidly to produce a stream of “ON” and “OFF” signals that can be converted into useful information. To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 06 ​Exploration Series ​ ​www.ck12.org Physics Concepts ​ |​ ​ ​Click on the link below to learn more. Gravity and Space Problems - ​http://www.ck12.org/physics/Gravity-and-Space-Problems/ Centripetal Force Problems - ​http://www.ck12.org/physics/Centripetal-Force-Problems/ Universal Law of Gravity - ​http://www.ck12.org/physics/Universal-Law-of-Gravity/ To access this physics simulation visit: ​ h​ ttp://goo.gl/hqKVbH ​ Page 07 .
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