00:02 Good day, class.

00:11 My name is Eme Nnamdi John.

00:13 I'll be taking your physics with a topic gravitational phase.

00:17 First, at the end of this lesson,

00:20 Lennon was able to learn one calculated gravitational force

00:23 between masses, calculated gravitational force

00:25 between two planets, explain G as a universal concept,

00:30 relates Kepler-Law to the motion of this solar system,

00:35 distinguished between natural and artificial satellites,

00:39 explain the concept of escape velocity.

00:45 First, what is field?

00:49 Field is a region where forces are being experienced.

00:52 Now, because we want to look about gravitational feed,

00:54 what is gravitational feed?

00:56 Draftational feed is a region

00:57 where gravitational forces are being experienced.

01:00 Now, on our gravitational field,

01:01 we're talking about what the law of gravitational,

01:03 which is by Isaac Newton,

01:08 we state that what force is that is proportional towards

01:13 to the masses, M1 and M2,

01:16 that is the first law, second law states that what,

01:18 force is inversely proportional towards,

01:20 inversely proportional to the square of the distance apart.

01:23 Now, if I might apply these two together,

01:26 I will say that what that force is the proportional

01:28 to the masses, M1 and M2,

01:31 an inversely proportional to the square

01:33 of the distance apart.

01:35 Now, what are we trying to see?

01:36 From this side, I will remove this word that F is equal

01:39 towards big G, M1, M2, over R2.

01:47 Now, this relationship or this is the two laws

01:52 of Isaac Newton, which is what,

01:54 the first one, which is what, whereby what the force

01:57 is that is proportional towards to the masses, M1 and M2,

02:00 whereby the force is inversely proportional towards

02:03 to the square of the distance apart.

02:05 Now, if we put these at one, we say that what,

02:07 that gravitational force or the law of gravitational force,

02:10 state that what, that the masses, M1 and M2,

02:14 is the proportional to the masses,

02:16 and inversely proportional to the square of the distance apart.

02:19 Now, from here, we have the G, which is the constant,

02:25 the G as the constant, the G as the constant.

02:30 Sometimes, we might be giving a question whereby,

02:33 we are giving only just a mass or a mass is giving to us.

02:36 Now, what are we going to do is to say that what,

02:38 that M1 is equal to what, M2 or M2 is equal to what, M1.

02:45 Now, by this, now, it simply means, I can say that what,

02:48 M1 is equal to M2 and M2 is equal to M1.

02:51 So, by so doing, I can say that what, that F,

02:55 which is the force, F, which is the force, is equal to what?

02:58 M1 dot M1 dot G, which is what, the gravitational constant,

03:06 over the square of the distance apart.

03:09 Now, this multiply by this, we have, as F, is equal to what,

03:14 M1 is equal to G over R2, which is the same thing as what,

03:19 as F is equal to what, G, M2 over R square.

03:24 Now, this is when we are giving a single mass,

03:31 when we are giving a single mass.

03:34 Now, by this, we can be able to get the gravitational constant,

03:37 which is what, G is equal to 6.67 times terrestrial minus what,

03:44 11.

03:47 There is a, the, the, the constants value for R.

03:54 Now, we can say, move down to talk about what,

03:56 gravitational intensity.

03:58 Now, what is gravitational intensity?

04:00 G is equal to what, F over M.

04:03 Now, this is gravitational intensity or oscillation due to gravity.

04:06 Now, what is the gravitational intensity?

04:08 This can be, or this is the ratio of the force over the mass.

04:11 Now, what is force?

04:13 We already have that, what's that force is equal to,

04:16 G is equal to, G, M1, M2 over R2.

04:21 Or, we can also say that what, that G is equal to M square over R square.

04:28 This is G.

04:30 Now, from this, I can impute this, this, to say that what,

04:33 G is equal to, big G, M1, M2 over R2 multiplied by M.

04:47 Now, I can say M1, this can take care of this.

04:55 I will have it, what, G is equal to a big G, M over R square.

05:03 Let's keep this one, it's very important.

05:06 Now, from this place, you can have relationship between the small G

05:09 with its oscillation due to gravity and the big G,

05:11 which is what, gravitational constants.

05:13 Now, I can say, make gravitational constants,

05:15 to be the subject of the formula, which I will have to be,

05:19 G R square is equal to, G, big G, M divided by M,

05:29 this can take care of G's.

05:31 So, therefore, we have a lot of, big G is equal to,

05:35 G R square, M comes to M, we have,

05:41 G is equal to, small G R square over, over M.

05:49 By so doing, we have these as, big G.

05:54 Okay, from this place, we will explain this, we've done this,

06:01 we'll explain this, we'll explain the gravitational intensity

06:06 of oscillation due to gravity.

06:10 Now, similarly, we can also say that, what,

06:14 from here, we can make here the R,

06:17 to be the, the radius of the 8th and also the M radius of 8th,

06:29 and the small M as, mass of 8th.

06:40 Now, which will give us, as, G is equal to, small G,

06:53 radius of the 8th, over, mass of the 8th.

07:01 I can block and keep it somewhere,

07:03 which is very important to us.

07:05 And I also say that, what?

07:07 That small G is equal to, the big G,

07:12 mass of the 8th, over, radius, square of the 8th.

07:18 We can see, keep this one as, also, another formula A.

07:22 Now, let's proceed, mass of the 8th, we'll explain that.

07:29 Okay, now, from gravitational potential,

07:35 from gravitational potential.

07:36 Now, what is gravitational potential?

07:39 This is the work done in resin, a unit chart of mass,

07:41 or this is the work done in resin, in mass,

07:44 from a ground surface to a height above, above the ground.

07:49 Now, from here, we can also say that, what,

07:51 that gravity is not constant, or gravitational potential,

07:54 can divide as a point, or the work done in moving a unit chart,

07:57 from infinity to a point of consideration.

08:02 Now, you can see that there is a negative function from the formula,

08:07 which you have that, we have it to be what the V is equal to,

08:11 minus G, M, over what R.

08:15 Now, this, that is, here, is a negative function,

08:20 which indicates an infinity sign, or the zero sign,

08:24 it indicates that, in this infinity sign, here,

08:28 which is infinity sign, which is higher than the potential,

08:30 or close to the mass, which you have this,

08:35 as the gravitational potential.

08:37 We have this, the negative sign, should be there.

08:41 Now, let's talk about the solar system.

08:49 Now, under the solar system, it consists

08:51 of the sun and the celestial bodies.

08:53 Now, we know all the celestial bodies, like the moon,

08:56 the moon is not, like the, the sun, we have the sun,

09:00 we have the Mercury, we have the Veno, we have the Pluto,

09:03 and others that are there.

09:05 And what we have here, on the screen, we have what,

09:08 that this consists of the sun and the celestial bodies,

09:10 objects, or bodies, we can call it a body,

09:13 or we can call it an object, around it,

09:16 and bound to eat by gravity.

09:19 That means, they are being guided by what it's gravity,

09:22 because it's at a point, at a point.

09:27 Now, the sun and other celestial bodies are around the sun,

09:32 around the sun, other celestial bodies are around this sun.

09:37 Now, we have that, the planet starts,

09:40 which one nearest to the sun, which is the Mercury,

09:42 the one nearest to the sun is what, the Mercury,

09:45 we have the Mercury, we have the Veno, we have the H,

09:47 we have the mass, these are the four that are closer to the H,

09:51 sorry, that are closer to the sun.

09:55 Now, like I explained, there are four small inner planets,

10:00 like the Mercury, the Veno, and the H, the mass.

10:03 These are called terrestrial bodies, or terrestrial planets.

10:07 All right, we'll be talking about the Kepler law.

10:14 This law describes the orbits of objects about the sun.

10:18 Now, we're talking about the fourth one,

10:20 that the planets each travel along an eclipse,

10:24 with the sun at one focose.

10:27 Now, look at the sun.

10:29 The sun is the other planets are focusing on the sun.

10:34 That's what the first law is trying to tell us.

10:36 These are sun, these are other, let's say, these Mercury,

10:41 these Veno, these are H, these mass,

10:45 these Jupiter, for instance.

10:47 All these are focusing to the sun.

10:50 Number two, we're two that's what,

10:53 that the line, join the sun and the planet,

10:56 sweep out equal area in equal time.

10:59 Now, this one, we have these as the planet already,

11:04 which is already given to roast.

11:07 Now, the total set of words, that the square of the period

11:10 of revolution of the planet are proportional to the cube

11:15 of their means, distance from the sun.

11:19 That means we have that what, which is the period,

11:23 is the repercussion to the distance,

11:27 which is what, the cube of the distance.

11:30 Simply means we can have it like this, as the period,

11:33 the square of the period is the repercussion of the word,

11:36 to the cube root of the distance.

11:40 Now, we're talking about the natural

11:45 and the artificial satellite.

11:47 Now, what are natural satellites?

11:49 Now, natural satellites are the special bodies,

11:54 like the moon.

11:54 These are, they are not being made by man.

11:58 They are just natural from creation, like the moon.

12:02 The moon is not being created by any man.

12:05 It's not being created by any man.

12:06 These are what we call natural satellites.

12:09 Moon is a satellite.

12:10 It is, the satellite for the eggs.

12:15 It is a satellite for the eggs, which is what the moon.

12:17 It's not being created by any man.

12:19 Not being created by any boy.

12:20 It's being created from origin.

12:22 Why artificial are those things that are being created by man?

12:26 A lot of things are being created by man.

12:27 Things are being created by man.

12:29 That is what we mean by what artificial satellites.

12:32 Now, we can talk about the SK Velos.

12:37 Or let's talk about the difference between the natural

12:40 and the artificial satellite.

12:43 Now, one of the differences is that,

12:45 natural is not man-made.

12:50 Why artificial are man-made?

12:53 SK Velocity.

12:54 This is the minimal velocity required for an object

13:01 to just escape from the gravitational influence.

13:04 Now, from there, we have that word.

13:10 That MV square X over R is equal to the force.

13:20 Now, what is our force?

13:21 Force, from the initial, what we are giving us,

13:24 force of the egg, we have that word, that G, M1, M2, over R2.

13:31 Now, I can substitute this G into this value.

13:35 I'll have it to watch.

13:41 I'll have it to be MV square X over R.

13:52 It's equal to the force, giving to us,

13:55 which is G, M1, M2, over R2.

14:02 Now, I can take care of this.

14:03 One of these can take care of this.

14:06 Then, I'll have it to be MV square X is equal to G12.

14:22 Now, I can take care of this and also take care of this.

14:26 I have it as what's R, which we give us as what's VX square

14:32 is equal to G M over R.

14:39 Like I said before, I can substitute the M to be the mass of the X.

14:46 Then, I'll have it to be VX square is equal to G M of the X over R.

14:57 Now, let's make V, the subject of the formula,

15:00 which we give us that VX is equal to the square root of G M e over R.

15:10 Now, this is what we need to know on the escape velocity.

15:21 Then, we can talk about the work done in carrying a mass from a point at a distance,

15:29 at a distance from the center of the edge to the distance.

15:33 So, let's get something from here.

15:43 Now, from this side, we have the force, which is equal to G M1, M2 over R2.

15:53 I'm simplifying these as our force.

15:57 Now, what is work done?

15:58 Work done is force times distance.

16:02 The work done is equal to force times distance.

16:12 Now, distance, which is what's work done, is equal to force times distance.

16:18 Now, force, we are already giving us force is equal to G M1, M2 over R2.

16:27 Now, make D as R, which is what the distance, we have towards work done is equal to what

16:38 work done is equal to force, which we are given as what G as G M1, M2 over R2, multiply by

16:52 the distance, which is R.

16:54 This can take care of this.

16:57 By so doing, we have our work done, which give us work done is equal to big G M1, M2 over

17:06 R, which we produced here.

17:12 Now, we can say from kinetic energy, from kinetic energy, which is, from kinetic energy

17:24 which is half MV square, now, let's impute this, making the kinetic energy equal to this,

17:43 we have what's the work done, work done is equal to kinetic energy.

17:55 Now what is our work done, we have the G M1, M2 over R is equal to kinetic energy, which

18:05 is one over two MV square, now, I can take care of this M, I can take care of this

18:12 M. Now, take this to this side, I'll have it towards 2G M over R is equal to V square.

18:29 Alright, from this place now, we have that what the V square, which is equal to 2G M over

18:41 R.

18:42 Now, make V, the subject of the formula, we have the V is equal to the square root of 2G M

18:53 over R, we give us this, now, let's look at from G is equal to big G M over R, from this,

19:11 from this point we can produce or get this, which is G is equal to, let's get by the formula

19:24 for that, to help us impute, okay, let's go, we can get it, alright, from this place, okay,

19:49 let's say from this we have both, both, the mass of H is equal to G R square over G, now

20:04 we can impute something into this place, now, what are we going to do from this place,

20:09 I can take either this to put it or I can take this to make the subject of the formula,

20:14 now, what am I going to do to make this any of this a subject of the formula, let's make

20:19 M as this, impute M into this place, I will have it to be, to be this, we already have

20:27 mass of H to be this, we have that V is equal to the square root of this, which will give

20:33 us to G over R, multiply the mass, which is given to us as G R square over big G, big

20:45 G comes to big G, R comes to R, then we have as what as V is equal to the square root of

20:53 2 G R, by this we have produced the escape velocity, we have produced the escape velocity,

21:05 now from here, which you have that R, that's R, R E is what is reduced, reduced of DX, all

21:24 right, from questions, let's take question from this, now the question is, two objects of

21:32 masses, seven KG and six KG are separated by distance of 0.2 m, if the gravitational constant

21:41 is 6.67 times theta square 11 Kg square, calculate the gravitational attraction between

21:51 them, now the first thing we have to do is to know the parameters given to R, without the

21:56 parameters you can be able to solve questions like this, now what are those parameters given

22:03 to R? First we are giving two masses, which are M1, which is what, we have the M1 which

22:09 is 70 Kg and M2 which is 60 Kg, now we are giving that it's been separated by a distance

22:22 of 0.2 m distance, which is R 0.2 m, now we are giving the gravitational constant as G

22:33 to be given us 6.67 times theta square minus 11, now what are we actually look for, we are

22:42 actually look for the force, and the force is not given to the force, now let's recall

22:47 from the formula, which is F is equal to G M1 M2 over R2, now we cannot impute the necessary

23:00 chain given to R, the G we are giving us, the G we are giving us F is equal to 6.67 times

23:15 10 minus 11 times M1 which we are giving us 70 times 60 over 0.2 or square, now we have

23:31 this as F is equal to 6.67 times 10 to the power minus 11 times, this time this we give

23:43 us 42, 1, 2 we give us 1, 2 over 0.2 or square, now from this side I can take care of this

23:56 as 1, 2, 2 or this one we are taking off, which we have that F is equal to 6.67 times 10

24:06 to the power minus 9 times 42 over 0.2 or square, all right let's use a calculator from

24:19 here, now let's get this, 6.67 times 42 times 10 raise to the power, let's have this

24:49 42 times 6.67 or give us as we have this 28 0.14 times 10 raise to the power minus 9, over

25:13 now let's get 0.2 times 0.2 give us 0.0.04, now 2.8 points 1 for divided by 0.04

25:41 now give us, now give us our fourth is equal to 7.003.5 times 10 raise to the power minus 9,

26:05 now I can have it to the power 1, 2 to be F is equal to 7.0.035 times, if that is by 2 this

26:20 will reduce by 2 10 raise to the power minus 7 new team and that is the answer for the force,

26:32 so our like us to take the number 2 as our own SS size, number 3 also number 4, number 5 try

26:46 your best to use the formulas that are given to us to calculate the functions, thank you for

26:53 watching, I am Emina Di Jong, see you next time.