Gavity Physics 6B Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
GRAVITY Any pai of objects, anywhee in the univese, feel a utual attaction due to gavity. Thee ae no exceptions if you have ass, evey othe ass is attacted to you, and you ae attacted to evey othe ass. Look aound the oo eveybody hee is attacted to you! Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
GRAVITY Any pai of objects, anywhee in the univese, feel a utual attaction due to gavity. Thee ae no exceptions if you have ass, evey othe ass is attacted to you, and you ae attacted to evey othe ass. Look aound the oo eveybody hee is attacted to you! Newton s Law of Univesal Gavitation gives us a foula to calculate the attactive foce between objects: gav 1 G 1 and ae the asses, and is the cente-to-cente distance between the 1 G is the gavitational constant it s tiny: G 6.674*10-11 N /kg Use this foula to find the agnitude of the gavity foce. Use a diaga o coon sense to find the diection. The foce will always be towad the othe ass. on 1 1 1 on Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
GRAVITY Any pai of objects, anywhee in the univese, feel a utual attaction due to gavity. Thee ae no exceptions if you have ass, evey othe ass is attacted to you, and you ae attacted to evey othe ass. Look aound the oo eveybody hee is attacted to you! Newton s Law of Univesal Gavitation gives us a foula to calculate the attactive foce between objects: gav 1 G 1 and ae the asses, and is the cente-to-cente distance between the 1 G is the gavitational constant it s tiny: G 6.674*10-11 N /kg Use this foula to find the agnitude of the gavity foce. Use a diaga o coon sense to find the diection. The foce will always be towad the othe ass. *Note: If you ae dealing with spheical objects with unifo density (ou typical assuption) then you can petend all the ass is concentated at the cente. 1 on on 1 1 Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Ou foula will find the foces (we supply 1 gav G the diection fo looking at the diaga): Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Ou foula will find the foces (we supply 1 gav G the diection fo looking at the diaga): 4 0 11 N ( 6 10 kg)( 6 10 kg) Apes on H 6.67 10 kg 1 10 ( ) This is negative because the foce points to the left Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Ou foula will find the foces (we supply 1 gav G the diection fo looking at the diaga): 4 0 11 ( 6 10 kg)( 6 10 kg) 11 6.67 10 N Apes on H.4 10 N kg 1 10 ( ) This is negative because the foce points to the left Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Ou foula will find the foces (we supply 1 gav G the diection fo looking at the diaga): 4 0 11 ( 6 10 kg)( 6 10 kg) 11 6.67 10 N Apes on H.4 10 N kg 1 10 + 6.67 10 11N DP on H kg ( ) 5 0 ( 3 10 kg)( 6 10 kg) 1 ( 3 10 ) + 1.3 10 11 N This is negative because the foce points to the left This is positive because the foce points to the ight Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: Thee planets ae aligned as shown. The asses and distances ae given in the diaga. ind the net gavitational foce on planet H (the iddle one). 10 1 3 x 10 1 Apes on H DP on H Planet of the Apes: ass6 x 10 4 kg Planet Hollywood: ass6 x 10 0 kg Daily Planet: ass3 x 10 5 kg Ou foula will find the foces (we supply 1 gav G the diection fo looking at the diaga): 4 0 11 ( 6 10 kg)( 6 10 kg) 11 6.67 10 N Apes on H.4 10 N kg 1 10 + 6.67 10 11N DP on H kg ( ) 5 0 ( 3 10 kg)( 6 10 kg) 1 ( 3 10 ) Add the foces to get the net foce on H: net + 1.3 10 11 11 1.1 10 N N This is negative because the foce points to the left This is positive because the foce points to the ight Net foce is to the left Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
One oe useful detail about gavity: GRAVITY The acceleation due to gavity on the suface of a planet is ight thee in the foula. Hee is the gavity foula, odified fo the case whee is the ass of an object on the suface of a planet. gav G planet ( R ) planet R planet Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
One oe useful detail about gavity: GRAVITY The acceleation due to gavity on the suface of a planet is ight thee in the foula. Hee is the gavity foula, odified fo the case whee is the ass of an object on the suface of a planet. gav G planet ( R ) planet We aleady know that gav is the weight of the object, and that should just be g (if the planet is the Eath) g G planet ( R ) planet R planet Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
One oe useful detail about gavity: GRAVITY The acceleation due to gavity on the suface of a planet is ight thee in the foula. Hee is the gavity foula, odified fo the case whee is the ass of an object on the suface of a planet. gav G planet ( R ) planet We aleady know that gav is the weight of the object, and that should just be g (if the planet is the Eath) g G planet ( R ) planet R planet This pat is g Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
1-3 Keple s Laws of Obital Motion Johannes Keple ade detailed studies of the appaent otions of the planets ove any yeas, and was able to foulate thee epiical laws: 1. Planets follow elliptical obits, with the Sun at one focus of the ellipse.
1-3 Keple s Laws of Obital Motion. As a planet oves in its obit, it sweeps out an equal aount of aea in an equal aount of tie.
1-3 Keple s Laws of Obital Motion 3. The peiod, T, of a planet inceases as its ean distance fo the Sun,, aised to the 3/ powe. This can be shown to be a consequence of the invese squae fo of the gavitational foce.
1-3 Keple s Laws of Obital Motion What should you use fo the constant?
1-3 Keple s Laws of Obital Motion What should you use fo the constant? Let s deive the foula to find out.
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. gav G 1
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. gav 1 G Notice that the gavity foce points towad the cente: i.e. it is the centipetal foce.
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. gav 1 G Notice that the gavity foce points towad the cente: i.e. it is the centipetal foce. We have a foula fo centipetal foce: cent v
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. Set these equal to get ou foula: M G v M is the ass of the cental object.
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. Set these equal to get ou foula: The ass of the obiting object will cancel out: M G v How do we get the peiod (T) involved in ou foula?
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. Set these equal to get ou foula: The ass of the obiting object will cancel out: M G v Each obit is one tip aound the cicle, so the distance taveled is. Speed is distance/tie, so we get: v π T
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. Set these equal to get ou foula: Plug in ou expession fo v: M G ( π T ) Now we can eaange this to solve fo T. Do this now.
1-3 Keple s Laws of Obital Motion Stat with Newton s Law of Gavity applied to a cicula obit. Set these equal to get ou foula: Plug in ou expession fo v: M G ( π T ) Now we can eaange this to solve fo T. Do this now. T π GM 3
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. a) Is Deios close to o fathe fo Mas than Phobos? Explain. Answe: Deios is fathe fo Mas. Inspection of the foula in Keple s 3 d Law should ake this clea. Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Peviously we deived an expession fo the constant. Ou foula is: T π GM 3 What do we use fo M in this foula? Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Peviously we deived an expession fo the constant. Ou foula is: T π GM 3 Hee M is the ass of the object being obited, in this case Mas. We can look this up in a table: M Mas 6.45x10 3 kg Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Peviously we deived an expession fo the constant. Ou foula is: T π GM 3 Hee M is the ass of the object being obited, in this case Mas. We can look this up in a table: M Mas 6.45x10 3 kg Reaange this foula to solve fo adius, then plug in the nubes: Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Peviously we deived an expession fo the constant. Ou foula is: T π GM 3 Hee M is the ass of the object being obited, in this case Mas. We can look this up in a table: M Mas 6.45x10 3 kg Reaange this foula to solve fo adius, then plug in the nubes: 3 GM 4π 3 T Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB
Exaple: The Matian oon Deios has an obital peiod that is geate than the othe Matian oon, Phobos. Both oons have appoxiately cicula obits. a) Is Deios close to o fathe fo Mas than Phobos? Explain. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x10 5 s. b) Calculate the distance fo the cente of Mas to Deios given that its peiod is 1.1x105 s. We will use the foula in Keple s 3 d Law fo this one, but we will need to figue out the constant. Peviously we deived an expession fo the constant. Ou foula is: T π GM 3 Hee M is the ass of the object being obited, in this case Mas. We can look this up in a table: M Mas 6.45x10 3 kg Reaange this foula to solve fo adius, then plug in the nubes: 3 GM 4π T 3 3 (6.67 10 11 N kg 4π )(6.45 10 3 kg) (1.10 10 5 s) 3.36 10 7 Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB