Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw of Motion www.njctl.og 2 Gvittionl Foce It hs been well known since ncient times tht Eth is sphee nd objects tht e ne the sufce tend fll down. https://www.njctl.og/video/?v=ip_u0xqvp04 ontents Jul 25 9:23 M Oct 10 8:20 M Newton connected the ide tht objects, like pples, fll towds the cente of Eth with the ide tht the moon obits ound Eth...it's lso flling towds the cente of Eth. The moon just stys in cicul motion since it hs velocity pependicul to its cceletion. Newton concluded tht ll objects ttct one nothe with "gvittionl foce". The mgnitude of the gvittionl foce deceses s the centes of the msses inceses in distnce. MORE Gvittionl ttction M 1 M 2 M 1 LESS Gvittionl ttction M 2 https://www.njctl.og/video/?v=uhs8k4gfu4s Oct 10 8:20 M Oct 10 8:20 M 1
Gvittionl onstnt G = 6.67 x 10 11 N m 2 /kg 2 In 1798, Heny vendish mesued G using tosion bem blnce. He did not initilly set out to mesue G, he ws insted tying to mesue the density of the Eth. Mthemticlly, the mgnitude of the gvittionl foce deceses with the invese of the sque of the distnce between the centes of the msses nd in popotion to the poduct of the msses. https://www.njctl.og/video/?v=2pdiuok9nw Jun 3 5:30 PM Oct 10 8:20 M The diection of the foce is long the line connecting the centes of the two msses. Ech mss feels foce of ttction towds the othe mss...long tht line. Newton's thid lw tells us tht the foce on ech mss is equl. Tht mens tht if I dop pen, the foce of Eth pulling the pen down is equl to the foce of the pen pulling Eth up. Howeve, since the mss of Eth is so much lge, tht foce cuses the pen to ccelete down, while the movement of Eth up is completely unmesuble. Oct 10 8:20 M Oct 10 8:20 M 1 Wht is the mgnitude of the gvittionl foce between two 1 kg objects which e locted 1.0 m pt? 2 Wht is the mgnitude of the gvittionl foce cting on 1.0 kg object which is 1.0 m fom 4.0 kg object? 3.3 x 10 11 N 1.7 x 10 11 N 2.7 x 10 10 N 6.7 x 10 11 N 3.3 x 10 11 N 1.7 x 10 11 N 2.7 x 10 10 N 6.7 x 10 11 N https://www.njctl.og/video/?v=ioovjt1i8lc https://www.njctl.og/video/?v=ip_u0xqvp04 2
3 Wht is the mgnitude of the gvittionl foce between Eth nd its moon? = 3.8 x 10 8 m m Eth = 6.0 x 10 24 kg m moon = 7.3 x 10 22 kg 4 Wht is the mgnitude of the gvittionl foce between Eth nd its sun? = 1.5 x 10 11 m m Eth = 6.0 x 10 24 kg m sun = 2.0 x 10 30 kg 2.0 x 10 18 N 2.0 x 10 19 N 2.0 x 10 20 N 2.0 x 10 21 N 3.6 x 10 18 N 3.6 x 10 19 N 3.6 x 10 21 N 3.6 x 10 22 N https://www.njctl.og/video/?v=m5goxjjge https://www.njctl.og/video/?v=4mien1t4yc Gvittionl Field Gvittionl Field While the foce between two objects cn lwys be computed by using the fomul fo FG; it's sometimes convenient to conside one mss s ceting gvittionl field nd the othe mss esponding to tht field. https://www.njctl.og/video/?v=p_oterhssk ontents Jul 25 9:23 M Nov 25 8:33 M Gvittionl Field The mgnitude of the gvittionl field ceted by n object vies fom loction to loction in spce; it depends on the distnce fom the object nd the object's mss. Gvittionl field, g, is vecto. It's diection is lwys towds the object ceting the field. Gvittionl Field 5 Whee is the gvittionl field the stongest? E Tht's the diection of the foce tht test mss would expeience if plced t tht loction. In fct, g is the cceletion tht mss would expeience if plced t tht loction in spce. Nov 25 8:33 M Nov 25 8:34 M 3
6 Wht hppens to the gvittionl field if the distnce fom the cente of n object doubles? 7 Wht hppens to the gvittionl field if the mss of n object doubles? It doubles It quduples It is cut to one hlf It is cut to one fouth It doubles It quduples It is cut to one hlf It is cut to one fouth https://www.njctl.og/video/?v=e1kr_75yl Sufce Gvity Plnets, sts, moons, ll hve gvittionl field...since they ll hve mss. Sufce Gvity ontents Tht field is lgest t the object's sufce, whee the distnce fom the cente of the object is the smllest...when "" is the dius of the object. y the wy, only the mss of the plnet tht's close to the cente of the plnet thn you e contibutes to its gvittionl field. So the field ctully gets smlle if you tunnel down below the sufce. M R Jul 25 9:23 M Nov 25 8:33 M 8 etemine the sufce gvity of Eth. Its mss is 6.0 x 10 24 kg nd its dius is 6.4 x 10 6 m. 9 etemine the sufce gvity of Eth's moon. Its mss is 7.4 x 10 kg nd its dius is 1.7 x 10 m. 22 6 https://www.njctl.og/video/?v=oc8zz7mnfte https://www.njctl.og/video/?v=r63pghowbv8 Nov 30 1:25 PM Nov 30 1:25 PM 4
10 ompute g fo the sufce of plnet whose dius is double tht of the Eth nd whose mss is tiple tht of Eth. Gvittionl Field in Spce ontents https://www.njctl.og/video/?v=iuwtyr2gxsq ec 1 5:09 PM Jul 25 9:23 M Gvittionl field in spce While gvity gets weke s you get fthe fom plnet, it neve becomes zeo. Thee is lwys some gvittionl field pesent due to evey plnet, st nd moon in the univese. The locl gvittionl field is usully dominted by neby msses since gvity gets weke s the invese sque of the distnce. The contibution of plnet to the locl gvittionl field cn be clculted using the sme eqution we've been using. You just hve to be ceful bout "". Gvittionl field in spce Nov 25 8:33 M Nov 25 8:33 M Gvittionl field in spce The contibution of plnet to the locl gvittionl field cn be clculted using the sme eqution we've been using. You just hve to be ceful bout "". 11 etemine the gvittionl field of Eth t height of 6.4 x 10 6 m (1 Eth dius). Eth's mss is 6.0 x 10 24 kg nd its dius is 6.4 x 10 6 m. If loction, "", is height "h" bove plnet of dius "R", it is distnce "" fom the plnet's cente, whee = R + h. R M h https://www.njctl.og/video/?v=7z_z2l53vs Nov 25 8:33 M Nov 30 1:25 PM 5
12 etemine the gvittionl field of Eth t height 2.88 x 10 8 m bove its sufce (the height of the moon bove Eth). Eth's mss is 6.0 x 10 24 kg nd its dius is 6.4 x 10 6 m. The Intentionl Spce Sttion (ISS) The Intentionl Spce Sttion (ISS) is esech fcility, the onobit constuction of which begn in 1998. The spce sttion is in Low Eth Obit nd cn be seen fom Eth with the nked eye! It obits t n ltitude of ppoximtely 350 km (190 mi) bove the sufce of the Eth, nd tvels t n vege speed of 27,700 kilometes (17,210 mi) pe hou. This mens the stonuts see 15 sunises eveydy! https://www.njctl.og/video/?v=q_esi6tz1yk https://www.njctl.og/video/?v=4kysw9_xhi0 Nov 30 1:25 PM Nov 30 1:42 PM 13 The occupnts of the Intentionl Spce Sttion (ISS) flot nd ppe to be weightless. etemine the stength of Eth's gvittionl field cting on stonuts in the ISS. 14 How does the gvittionl field cting on the occupnts in the spce sttion compe to the gvittionl field cting on you now? Eth's mss is 6.0 x 10 24 kg nd its dius is 6.4 x 10 6 m. The ISS is 350km (3.5 x 10 5 m) bove the sufce of Eth. It's the sme It's slightly less It's bout hlf s stong Thee is no gvity cting on them https://www.njctl.og/video/?v=4kysw9_xhi0 https://www.njctl.og/video/?v=gzf PTY Nov 30 1:42 PM Nov 30 1:54 PM R h We've ledy detemined tht the gvittionl field cting on the occupnts of the spce sttion, nd on the spce sttion itself, is not vey diffeent thn the foce cting on us. Eth ISS How come they don't fll to Eth? https://www.njctl.og/video/?v=h0inolrgm ontents This digm should look elly fmili. Jul 25 9:23 M 6
d Eth ISS The gvittionl field will be pointed towds the cente of Eth nd epesents the cceletion tht mss would expeience t tht loction (egdless of the mss). In this cse ny object would simply fll to Eth. How could tht be voided? v If the object hs tngentil velocity pependicul to its cceletion, it will go in cicle. It will keep flling to Eth, but neve stike Eth. https://www.njctl.og/video/?v=iqohrkknnlq Hee is Newton's own dwing of thought expeiment whee cnnon on vey high mountin (bove the tmosphee) shoots shell with incesing speed, shown by tjectoies fo the shell of, E, F, nd G nd finlly so fst tht it neve flls to eth, but goes into obit. v We cn clculte the velocity necessy to mintin stble obit t distnce "" fom the cente of plnet of mss "M". https://www.njctl.og/video/?v=oizv ixrtcy https://www.njctl.og/video/?v=h0inolrgm Nov 30 8:06 PM Fom tht, we cn clculte the peiod, T, of ny object's obit. 15 ompute g t distnce of 7.3 x 10 8 m fom the cente of spheicl object whose mss is 3.0 x 10 27 kg. o v https://www.njctl.og/video/?v=mrie_t_eg ec 1 5:15 PM 7
16 Use you pevious nswe to detemine the velocity, both mgnitude nd diection, fo n object obiting t distnce of 7.3 x 10 8 m fom the cente of spheicl object whose mss is 3.0 x 10 27 kg. 17 Use you pevious nswe to detemine the obitl peiod of fo n object obiting t distnce of 7.3 x 10 8 m fom the cente of spheicl object whose mss is 3.0 x 10 27 kg. https://www.njctl.og/video/?v=kwb0u Y4Jg https://www.njctl.og/video/?v=5m1umwl5li ec 1 5:15 PM ec 1 5:16 PM 18 ompute g t height of 59 eth dii bove the sufce of Eth. 19 Use you pevious nswe to detemine the velocity, both mgnitude nd diection, fo n object obiting t height of 59 R E bove the sufce of Eth. View solution https://youtu.be/dqujso8tm ec 1 5:16 PM ec 1 5:16 PM 20 Use you pevious nswe to detemine the obitl peiod of n object obiting t height of 59 R E bove the sufce of Eth. Keple's Thid Lw of Motion https://www.njctl.og/video/?v=5v5iqyyy ontents ec 1 5:17 PM Jul 25 9:23 M 8
Now, we cn find the eltionship between the peiod, T, nd the obitl dius,, fo ny obit. Keple's Thid Lw v Keple hd noted tht the tio of T 2 / 3 yields the sme esult fo ll the plnets. Tht is, the sque of the peiod of ny plnet's obit divided by the cube of its distnce fom the sun lwys yields the sme numbe. We hve now shown why: (4π 2 ) / (GM) is constnt; its the sme fo ll obiting objects, whee M is the mss of the object being obited; it is independent of the object tht is obiting. Keple's Thid Lw If you know the peiod (T) of plnet's obit, you cn detemine its distnce () fom the sun. Since ll plnets obiting the sun hve the sme peiod to distnce tio, the following is tue: 21 The peiod of the Moon is 27.3 dys nd its obitl dius is 3.8 x 10 m. Wht would be the obitl 8 dius of n object obiting Eth with peiod of 20 dys? T(white) 2 T(geen) 2 = (white) 3 (geen)3 https://www.njctl.og/video/?v=eqzmy3p5cyc Jun 3 7:14 PM Jul 22 11:39 M 22 Wht is the obitl peiod (in dys) of n unknown object obiting the sun with n obitl dius of twice tht of eth? https://www.njctl.og/video/?v=itqif01ytnq Jul 22 12:22 PM Feb 15 12:43 PM 9