6.2. orbits. Satellites and Space Stations

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1 obits RADARSAT-1 and RADARSAT-2 ae Eath-obsevation satellites designed and commissioned by the Canadian Space Agency. These eyes in the skies pee down fom obit, captuing images and data that help scientists monito envionmental changes and the planet s natual esouces. Examples of satellite monitoing include detecting oil spills, tacking ice movements, identifying ships at sea, and monitoing natual disastes. Figue 1 shows an image of RADARSAT Figue 1 RADARSAT-2 uses sophisticated micowave-based ada to collect images of Eath day and night, even though cloud cove. Satellites and Space Stations A satellite is an object o a body that evolves aound anothe body that usually has much moe mass than the satellite. Fo example, the planets ae natual satellites evolving aound the Sun. Planetay moons, including Eath s moon, ae natual satellites, too. Atificial satellites, on the othe hand, ae human-made objects that obit Eath o othe bodies in the sola system. CAREER LINK RADARSAT-1 and RADARSAT-2 ae examples of atificial satellites. Anothe wellknown example of atificial satellites is the netwok of 24 satellites that make up the Global Positioning System (GPS). By coodinating seveal signals at once, as shown in Figue 2, the system can locate an object on Eath s suface to within 15 m of its actual position. satellite an object o a body that evolves aound anothe body due to gavitational attaction atificial satellite an object that has been intentionally placed by humans into obit aound Eath o anothe body; efeed to as atifi cial to distinguish fom natual satellites such as the Moon S 1 S 1 S 2 S 1 S 2 S 3 (a) (b) (c) Figue 2 GPS satellites can detemine the location of an object, in this case a boat. (a) The data fom one satellite will show that the location is somewhee along the cicumfeence of a cicle. (b) Two satellites consulted simultaneously will efi ne the location to one of two intesection spots. (c) With thee satellites consulted simultaneously, the intesection of thee cicles will give the location of the boat to within 15 m of its actual position. 6.2 Obits 297

2 space station a spacecaft in which people live and wok Figue 3 The Intenational Space Station is an obiting spacecaft in which astonauts live and wok in space. The boat shown in Figue 2 on the pevious page has a compute-contolled GPS eceive that detects signals fom thee satellites simultaneously. The system calculates distances based on signal speeds and tansmission times. A single satellite can identify the boat s location somewhee along the cicumfeence of a cicle. Two simultaneous satellite signals can pinpoint the location at one of two intesecting spots whee two cicles intesect. With a thid satellite and theefoe thee intesecting cicles the boat s location can be pinpointed. This is efeed to as tiangulation. Anothe example of an atificial satellite in Eath obit is a space station, a spacecaft in which people live and wok. An example is the Intenational Space Station (ISS), shown in Figue 3. The ISS is a pemanent obiting laboatoy that suppots many diffeent eseach pojects. In the pocess, scientists ae also able to study human esponses to space tavel and zeo gavity o, moe accuately, micogavity: times the value of g. A micogavity envionment is pesent when any object is in fee fall. So when you dive fom a dive towe into a swimming pool, you ae in micogavity until you hit the wate. Similaly, astonauts aboad the ISS ae in a constant state of fee fall and ae thus in a micogavity envionment. It is impotant to note the diffeence between micogavity and the gavitational field stength, since the value of g at the altitude of the ISS is appoximately 8.7 N/kg. Clealy, thee is still a significant gavitational foce at that altitude and it is incoect to say that the astonauts ae in zeo gavity. A gavitational foce of appoximately zeo would only occu if you wee extemely fa away fom any mass. The knowledge gained fom eseach by obiting space stations enables scientists to design spacecaft that can safely tanspot people though space and pefom expeiments in micogavity envionments. These micogavity expeiments can lead to beakthoughs in medicine and chemisty. CAREER LINK Mini Investigation Exploing Gavity and Obits Mini Investigation Skills: Pefoming, Obseving, Analyzing, Communicating In this investigation, you will use a simulation to ceate and exploe diffeent configuations of obiting bodies. Move the planets, moons, o the Sun to see how the obital paths change. Change the sizes of the objects and the distances between them. Exploe the vaiations that occu as the foce of gavity is changed o when gavity is emoved fom the model. Equipment and Mateials: compute with Intenet access 1. Go to the Nelson Science website. 2. Load the suppoting softwae, if necessay. 3. Select the option to view the Sun, Eath, and Moon and the options to show Gavity Foce and the Path. 4. Play the simulation and allow Eath to complete one full evolution aound the Sun. 5. Pause the simulation. 6. Using the slide ba, incease the size of the Sun and stat the simulation again. Obseve the motion of Eath and the Moon aound the Sun fo one full evolution. 7. Pause the simulation again. Retun the Sun to its oiginal size and then incease the size of Eath. 8. Stat the simulation again and obseve Eath s evolution. A. What happens to the obit of Eath when you incease the size of the Sun? T/I A B. What happens to the Moon when you incease the size of the Sun? What happens when you incease the size of Eath? T/I A C. What happens to Eath s obit when you incease the size of Eath? T/I A D. The MESSENGER pobe mentioned at the beginning of this chapte made use of seveal gavity assists to each Mecuy without using too much of its own enegy. This method is also known as a gavitational slingshot. It woks by using the gavity of a celestial body to acceleate, slow down, o ediect the path of a spacecaft. Gavity assists can save fuel, time, and expense. Ty to design a system of obiting elements within the simulation that demonstates this effect. K/U T/I C A WEB LINK 298 Chapte 6 Gavitational Fields

3 Satellites in Cicula Obits When Newton developed the idea of univesal gavitation, he also theoized that the same foce that pulls objects to Eath also keeps the Moon in its obit. One diffeence, of couse, is that the Moon does not hit Eath s suface. The Moon obits Eath at a distance fom Eath s cente called the obital adius. The obit of the Moon about Eath is anothe example of centipetal motion, which you studied in Chapte 3. The foce of gavity on the Moon due to Eath is a centipetal foce that pulls the Moon towad Eath s cente. As the Moon obits Eath, the Moon has velocity pependicula to the adius vecto. Without gavity, the Moon would fly off in a staight line. Without its obital velocity, howeve, the foce of gavity would pull the Moon staight to Eath s suface. The obital motion of the Moon depends on both the centipetal foce due to gavity and the Moon s obital velocity. The Moon s obit, simila to the obits of the planets aound the Sun, is actually elliptical. We can closely appoximate the obits, howeve, by assuming that they ae cicula. This appoximation is useful fo most poblem-solving puposes. To analyze the motion of a satellite in unifom cicula motion, combine Newton s law of univesal gavitation with the mathematical expession descibing centipetal acceleation. Using the univesal law of gavitation fom Section 6.1, we can say that the gavitational field stength of Eath with mass m E at the location of a satellite at height above Eath s cente is obital adius the distance between the cente of a satellite and the cente of its paent body g 5 Gm E 2 Recall fom Chapte 3 that the fomula fo centipetal acceleation based on the obiting object s speed v is a c 5 v 2 Fo a satellite in a cicula obit, the gavitational foce povides the centipetal foce. Combining the above two equations gives a c 5 g v 2 5 Gm E 2 Unit TASK BOOKMARK You can apply what you have leaned about obits and satellites to the Unit Task on page 422. Solving fo the speed of the satellite and using only the positive squae oot gives v 5 Å Gm E This equation holds fo an obiting body in a cental gavitational field. If a satellite obits aound any othe lage body with mass m, we can eplace the mass of Eath in this equation and genealize it to v 5 Å Gm This equation indicates that the speed of a satellite depends on its obital adius and is independent of the satellite s own mass. Fo a satellite to maintain an obit of adius, its speed v must be constant. 6.2 Obits 299

4 geosynchonous obit the obit aound Eath of an object with an obital speed matching the ate of Eath s otation; the peiod of such an obit is exactly one Eath day A communications satellite in geosynchonous obit that is, a satellite obiting Eath with a speed matching that of Eath s own otation is an example of an atificial satellite with a constant obital adius (Figue 4). The obital peiod, epesented by the symbol T, is the time it takes an object to complete one obit aound anothe object. A geosynchonous satellite s obital speed leads to an obital peiod that exactly matches Eath s otational peiod. To an obseve on Eath, the satellite will appea to tavel though the same point in the sky evey 24 h. A geostationay obit is a type of geosynchonous obit in which the satellite obits diectly ove the equato. To an obseve on Eath, a geostationay satellite will appea to emain fixed in the same point in the sky at all times. CAREER LINK adius foce of gavity Figue 4 A satellite with a geosynchonous obit tavels at the same speed as Eath s otation. Its obital peiod is one Eath day. In the following Tutoial you will exploe how you can use the equation fo obital speed in poblem solving. obit Tutoial 1 Solving Poblems Relating to Cicula Obits The Sample Poblems in this Tutoial show how to detemine the popeties of an object in a cicula obit within a gavitational field aound a lage object. Sample Poblem 1: Calculating the Speed and Obital Peiod of a Satellite The Intenational Space Station (ISS) obits Eath at an altitude of about 350 km above Eath s suface. (a) Detemine the speed needed by the ISS to maintain its obit. (b) Detemine the obital peiod of the ISS in minutes. Solution (a) Given: G N m 2 /kg 2 ; m E kg; E m; h ISS km m Requied: v Gm E Analysis: v 5 ; 5 Å E 1 h ISS m Solution: v 5 Å Gm E kg # m # m 2 s kg2 kg 2 5 ï m v m/s 1two exta digits caied2 Statement: The ISS equies a speed of m/s to maintain its obit. 300 Chapte 6 Gavitational Fields

5 (b) Given: v m/s; m Requied: T Analysis: The distance tavelled in one peiod is 2p. The obital peiod, T, is the time it takes fo the space station to tavel this distance, so it is the distance divided by the speed, T 5 2p. v Solution: T 5 2p v 5 2p m m 3 1 min 60 s 3 s T 5 92 min Statement: The ISS has an obital peiod of 92 min. Sample Poblem 2: Calculating the Speeds of Planets aound the Sun Detemine the speeds of Venus and Eath as they obit the Sun. The Sun s mass is kg. Venus has an obital adius of m, and Eath has an obital adius of m. Given: G N m 2 /kg 2 ; m S kg; V m; E m Requied: v V ; v E Gm Analysis: v 5 Å Solution: Gm S v V 5 Å V kg # m # m 2 s kg2 kg 2 5 ï m v V m/s Gm S v E 5 Å E kg # m # m 2 s kg2 kg 2 5 ï m v E m/s Statement: Venus obits the Sun at a speed of m/s, and Eath obits the Sun at a speed of m/s. 6.2 Obits 301

6 Pactice 1. Astonomes have detemined that a black hole sits at the cente of galaxy M87 (Figue 5). Obsevations show matte at a distance of m fom the black hole and tavelling at speeds of m/s. Calculate the mass of the black hole, assuming the matte being obseved moves in a cicula obit aound it. T/I A [ans: kg] Figue 5 Investigation Design a Sola System (page 309) With what you have leaned about obits and the movement of planetay bodies, you ae eady to take the next step. This investigation will give you an oppotunity to ceate you own sola system with a sun, seveal planets, and moons. 2. Mas obits the Sun in a nealy cicula obit of adius m. The mass of Mas is kg. Mas expeiences a gavitational foce fom the Sun of magnitude N. Calculate the speed of Mas and the peiod of evolution fo Mas in tems of Eath yeas. T/I A [ans: m/s; 1.90 Eath yeas] 3. Calculate the speed of a satellite in a cicula obit km above Eath s suface. Detemine the obital peiod of the satellite to two signifi cant digits. T/I A [ans: m/s; 97 min] 4. Satellites can obit the Moon vey close to the Moon s suface because the Moon has no atmosphee to slow the satellite though ai esistance. Detemine the speed of a satellite that obits the Moon just 25 m above the suface. (Hint: Refe to Appendix B fo adius and mass data fo the Moon.) T/I A [ans: m/s] eseach This Space Junk Skills: Reseaching, Analyzing, Communicating Space junk is debis fom atifi cial objects obiting Eath. It is just one example of how benefi cial technology can have unwanted envionmental effects. In this activity, you will eseach space junk and discove how an obiting body can go fom being a functioning satellite to being space junk. 1. Reseach the mechanisms that satellites have to maintain speed and obital adius. 2. Reseach methods of dealing with diffeent foms of space junk. 3. Exploe one stoy of space junk that catches you inteest. A. Review this chapte s fomulas petaining to the elationship between obital speed and obital adius. Descibe effects that could make a satellite slow down in its obit and slip into a lowe obit. C A SKILLS HANDBOOK A4.1 B. Descibe what happens when a satellite difts so low that it entes Eath s atmosphee. C A C. Ae thee any ways to avoid ceating space junk? T/I C D. Ae thee any effective ways to get id of existing space junk? C A E. Compose an to a fiend descibing what space junk is. Include the inteesting example you eseached in Step 3. C WEB LINK 302 Chapte 6 Gavitational Fields

7 6.2 Review Summay Satellites can be natual, such as moons aound planets, o atificial, such as the RADARSAT satellites and the Intenational Space Station. The speed, v, of a satellite in unifom cicula motion aound a cental body depends on the mass of the cental body, m, and the adius of the obit, : v 5 Å Gm Fo a given obital adius, a satellite in cicula obit has a constant speed. Questions 1. What is the diffeence between natual and atificial satellites? Give an example of each. K/U 2. Explain what micogavity is. K/U 3. Explain in you own wods how GPS satellites wok. K/U 4. (a) What is a geosynchonous obit? (b) How does a satellite in geosynchonous obit appea to an obseve on Eath? (c) How does a satellite in geostationay obit appea to an obseve on Eath? K/U C 5. Calculate the obital adius of a satellite in geosynchonous obit. K/U T/I A 6. Neptune obits the Sun in Eath yeas in an appoximately cicula obit at a adius of km. T/I A (a) Detemine the obital speed of Neptune. (b) Detemine the mass of the Sun. 7. Satun makes one complete obit of the Sun evey 29 Eath yeas with a speed of 9.69 km/s. Calculate the adius of the obit of Satun. Assume a cicula obit. T/I A 8. The egion of the sola system between Mas and Jupite, called the Asteoid Belt, contains many asteoids that obit the Sun. Conside an asteoid in a cicula obit of adius m. T/I A (a) Calculate the speed of the asteoid aound the Sun. (b) Calculate the peiod of the obit in yeas. 9. In ecent yeas, astonomes have discoveed that a numbe of neaby stas have planets of thei own, called exoplanets. A newly discoveed exoplanet obits a sta with ou Sun s mass ( kg) in a cicula obit with an obital adius of m. What is the obital speed of the exoplanet in kilometes pe hou? T/I A 10. The obital adius of one exoplanet is m, with a peiod of 1100 Eath days. Calculate the mass of the sta aound which the exoplanet evolves. T/I A 11. Phobos (Figue 6), one of Mas s moons, has an elliptical obit aound Mas with an obital adius that vaies between 9200 km and 9500 km. Calculate the obital peiod of Phobos in Eath days, assuming a cicula obit of adius m. The mass of Mas is kg. T/I A Figue Detemine the speed of a satellite, in kilometes pe hou, that is in a geosynchonous obit about Eath. (Hint: Use the equation fo the speed of an object in cicula motion and equate that to the speed of a satellite in obit aound a cental body. Reaange the equation to solve fo the adius. Use the adius to calculate the speed.) K/U T/I A 13. (a) Calculate the obital speeds of the planets Mecuy, Venus, Eath, and Mas using the sola system data in Appendix B. (b) What can you conclude about the speed of the planets in obit fathe fom the Sun? T/I A 14. Scientists wish to place a geosynchonous satellite nea a moon at an altitude of 410 km. The mass of the moon is kg and it has a adius of m. Calculate the velocity and the peiod of the satellite. T/I A 6.2 Obits 303