# Introduction to Newton’s law of gravitation | Physics | Khan Academy

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We’re now going to learn a

little bit about gravity. And just so you know, gravity is

something that, especially in introductory physics or

even reasonably advanced physics, we can learn how to

calculate it, we can learn how to realize what are the

important variables in it, but it’s something that’s really

not well understood. Even once you learn general

relativity, if you do get there, I have to say, you can

kind of say, oh, well, it’s the warping of space time and

all of this, but it’s hard to get an intuition of why two

objects, just because they have this thing called

mass, they are attracted to each other. It’s really, at least to me,

a little bit mystical. But with that said, let’s learn

to deal with gravity. And we’ll do that learning

Newton’s Law of Gravity, and this works for most purposes. So Newton’s Law of Gravity says

that the force between two masses, and that’s the

gravitational force, is equal to the gravitational constant G

times the mass of the first object times the mass of the

second object divided by the distance between the two

objects squared. So that’s simple enough. So let’s play around with this,

and see if we can get some results that look

reasonably familiar to us. So let’s use this formula

to figure out what the acceleration, the gravitational

acceleration, is at the surface of the Earth. So let’s draw the Earth,

just so we know what we’re talking about. So that’s my Earth. And let’s say we want to figure

out the gravitational acceleration on Sal. That’s me. And so how do we apply this

equation to figure out how much I’m accelerating down

towards the center of Earth or the Earth’s center of mass? The force is equal to– so

what’s this big G thing? The G is the universal

gravitational constant. Although, as far as I know, and

I’m not an expert on this, I actually think its measurement

can change. It’s not truly, truly a

constant, or I guess when on different scales, it can be

a little bit different. But for our purposes, it is a

constant, and the constant in most physics classes, is this:

6.67 times 10 to the negative 11th meters cubed per kilogram

seconds squared. I know these units are crazy,

but all you have to realize is these are just the units needed,

that when you multiply it times a mass and a mass

divided by a distance squared, you get Newtons, or kilogram

meters per second squared. So we won’t worry so much about

the units right now. Just realize that you’re going

to have to work with meters in kilograms seconds. So let’s just write

that number down. I’ll change colors to

keep it interesting. 6.67 times 10 to the negative

11th, and we want to know the acceleration on Sal, so

m1 is the mass of Sal. And I don’t feel like revealing

my mass in this video, so I’ll just leave

it as a variable. And then what’s the mass 2? It’s the mass of Earth. And I wrote that here. I looked it up on Wikipedia. This is the mass of Earth. So I multiply it times the

mass of Earth, times 5.97 times 10 to the 24th kilograms–

weighs a little bit, not weighs, is a little

bit more massive than Sal– divided by the distance

squared. Now, you might say, well, what’s

the distance between someone standing on the

Earth and the Earth? Well, it’s zero because they’re

touching the Earth. But it’s important to realize

that the distance between the two objects, especially when

we’re talking about the universal law of gravitation, is

the distance between their center of masses. For all general purposes, my

center of mass, maybe it’s like three feet above

the ground, because I’m not that tall. It’s probably a little bit lower

than that, actually. Anyway, my center of mass might

be three feet above the ground, and where’s Earth’s

center of mass? Well, it’s at the center of

Earth, so we have to know the radius of Earth, right? So the radius of Earth is–

I also looked it up on Wikipedia– 6,371 kilometers. How many meters is that? It’s 6 million meters, right? And then, you know, the extra

meter to get to my center of mass, we can ignore for now,

because it would be .001, so we’ll ignore that for now. So it’s 6– and soon. I’ll write it in scientific

notation since everything else is in scientific notation–

6.371 times 10 to the sixth meters, right? 6,000 kilometers is

6 million meters. So let’s write that down. So the distance is going

to be 6.37 times 10 to the sixth meters. We have to square that. Remember, it’s distance

squared. So let’s see if we can simplify

this a little bit. Let’s just multiply those top

numbers first. Force is equal to– let’s bring the

variable out. Mass of Sal times– let’s

do this top part. So we have 6.67 times 5.97

is equal to 39.82. And I just multiplied this times

this, so now I have to multiply the 10’s. So 10 to the negative 11th times

10 to the negative 24th. We can just add the exponents. They have the same base. So what’s 24 minus 11? It’s 10 to the 13th, right? And then what does the

denominator look like? It’s going to be the 6.37

squared times 10 to the sixth squared. So it’s going to be– whatever

this is is going to be like 37 or something– times– what’s

10 to the sixth squared? It’s 10 to the 12th, right? 10 to the 12th. So let’s figure out what

6.37 squared is. This little calculator I have

doesn’t have squared, so I have to– so it’s 40.58. And so simplifying it, the force

is equal to the mass of Sal times– let’s divide, 39.82

divided by 40.58 is equal to 9.81. That’s just this divided

by this. And then 10 to the 13th divided

by 10 to the 12th. Actually no, this isn’t 9.81. Sorry, it’s 0.981. 0.981, and then 10 to the 13th

divided by 10 to the 12th is just 10, right? 10 to the first, times 10,

so what’s 0.981 times 10? Well, the force is equal to 9.81

times the mass of Sal. And where does this get us? How can we figure out the

acceleration right now? Well, force is just mass times

acceleration, right? So that’s also going to just be

equal to the acceleration of gravity– that’s supposed to

be a small g there– times the mass of Sal, right? So we know the gravitational

force is 9.81 times the mass of Sal, and we also know that

that’s the same thing as the acceleration of gravity

times the mass of Sal. We can divide both sides by the

mass of Sal, and we have the acceleration of gravity. And if we had used the units the

whole way, you would have seen that it is kilograms meters

per second squared. And we have just shown that, at

least based on the numbers that they’ve given in Wikipedia,

the acceleration of gravity on the surface of the

Earth is almost exactly what we’ve been using in all the

projectile motion problems. It’s 9.8 meters per

second squared. That’s exciting. So let’s do another quick

problem with gravity, because I’ve got two minutes. Let’s say there’s another

planet called the planet Small Earth. And let’s say the radius of

Small Earth is equal to 1/2 the radius of Earth and the mass

of Small Earth is equal to 1/2 the mass of Earth. So what’s the pull of gravity

on any object, say same object, on this? How much smaller would

it be on this planet? Well, actually let me save

that to the next video, because I hate being rushed. So I’ll see you

dr9106Post authoryou people are two suck up, here is someone trying to teach something and all you ppl do is complain. i wanna see some of you even try to do better. Thanks for the explaination Sal, you cleared up some confusion.

dr9106Post authoro yea and for DaAfterburner, this is not a video for you, this is for people intrested in learning some physics, i can see you are surely ignorant, and lack maturity to have respect for other people's work. i can also see you are clearly not fit to even conceptualize the defination of physics, i pitty you.

Nine PhilimeterPost authorYou don't want to disclose your mass…wow…just wow.

MagicmanPost author…….u sound simple minded…Its a joke dude…if u watch the rest of his videos u'd understand he has a sense of humor >.>

MagicmanPost author@philster00700 ….and if you paid any attention…It was better to leave his mass as a variable as it helped prove that g = 9.81 as his mass just cancelled out

Aris MarkPost authorSal is that my calculator You using?…hehehe. hopeing this simple questions and solutions would help me on TTC test!..thanks….

KosekansPost authorotuonyec pointed out the real reason for leaving the mass variable and philster00700 … you're … wow … just wow… xD

Annie ArmstrongPost authoru r a very good teacher, thank you!!!!

how do u graph universal law of gravitation..if u have time could u maybe do a sample problem to graph?? 🙂

divvy1400yam600Post authorYou start the vid. by saying that objects attract one another by a mysterious force called gravity.

You then demonstrate the value of that force if object A acclelerates around object B .

Therfore it seems to me that the 'source' of gravity is acceleration. NOT the presence of the objects.

The equation F = m.A confirms this does it not ?

Travis TkachukPost author@divvy1400yam600 No it does not. The simplest explination I can think of is think of a large sheet (this is the space time continuum) and you place a bowling ball in said sheet (you can think of this as a planet or anything with mass really). You would observe that the sheet dips around the object. Now if you place a marble near the dip it would roll toward the object. A mass would effect the space time continuum same as the bowling ball does the sheet, and the dips are the force of gravity.

divvy1400yam600Post author@WannaBeAnEE You rascal. You read that in a book.

divvy1400yam600Post author@WannaBeAnEE You rascal. You read that in a book.

Incidently Stephan Hawkins has just been quoted as saying that gravity helped caus the Big Bang.

There appears to be no limit to to what it is tought gravity can do.

Does it really cause the tides on Earth ?

I dont think so….do you ?

Travis TkachukPost author@divvy1400yam600 I can assure you in all honesty I did not. Im going to have to look in on that Quote. The tides are caused by the gravational attraction between the earth and the moon.

Some food for thought though as strong as gravity is, in that it pulls you toward the earths center, it can easily be overcome. i.e. lifting a weight off the ground.

Chicken and WafflesPost authorumm what happened to your height why didnt you add that in the distance?3m?

Chicken and WafflesPost authorthanks a lot though this really helps me out1!!!:)

Amber LawsonPost authorall this was was a bunch of math equations! what the heck! i am solemnly disappionted!

Raf UziPost authorgreat video sal..thanx

Jonathan PalmerPost authorthis helped a lot… i stumbled across this literally the day we ended up going over it in class… so it ended up really helping me visualize the math involved.

Ambriz745Post authorGreat work. Thanks!

lupischucklePost authorThis is great! I'm currently writing a paper on Newton's alchemical influences on his explanation of gravity, and this is just a nice little video that helps me to better understand the laws of gravitation so I can know what it is I'm talking about. This makes for a deeper understanding of the subject matter, and a better paper. Physics helping History! Interdisciplinary action FTW! Thank you!!

LiamOHorriblePost authorgreat video Sal, thanks for posting… and an FYI for you: that little calculator program in your windows accessories-if you go to the view menu, you can switch it to scientific notation (much more useful!). thanks again…

LilgabbyjPost authorI love how you change colours to keep it interesting =)

Minky Tres-vainPost authorThank you. So, so much.

narpupPost authorit is funny when i thing of gravity i think of water because when thinks are liter then water they flat just like gravity

B1indfirePost authorSal, I know this is late, but if you go to "View" on the calculator, you can change it to scientific and have a squared button =D

P.S. You sould like one of my friends whose name is Sal… just older.

KanbeiPost authorHow does it feel to be able to cancel your mass?

Christophe ValahuPost authorSorry to report an error but when you do the (Mass of sal times 5.97 etc) divided by the rest, you cant transfer sal to the rite just as it is. You need to keep it as in expression such as M of Sal divided by 6.37 etc times the rest.

supermanuman95Post authormy physics teacher teached us that g is 9.8 n/kg, is that correct?

he has 6.67 x 10 (to the power of elen)

:S

John CocaboPost author@supermanuman95 Big G is the gravitational constant which is 6.67 x 10^-11 while small g is the gravitational force of the earth which is more or less 9.80 or 9.81 for fancy people.

Jose SuarezPost authorA gravitational force field consists of two sub fields. One is excursive which repels other worlds and establishes their orbital corridors, and the other is gravity which serves to coalesce and unify matter towards a concentric point from whence it radiates. Both fields accrue pressure starting at the plane of the exosphere but in opposite directions at a constant rate of .0735 pounds per sq. in. per linear mile of expansion. This is my theory and my calculations. Sir Newton was wrong!

anthony gaonaPost authorso would this some what prove that levitation is not possible?

Chantheman5Post authorwoah what has this guy done to u haters? Thanks sal ur great. I think the ones who hate you are some dumb white kids or some idiotic drop outs.

Chantheman5Post author6 retards disliked this

SSuperCurioussPost authorPLEAAAASEEEE continue this on to general relativity and include all the math.. the vids from Stanford uni are TERRIBLE !!!!

johnnytheprickPost author@ mr khan of khan academy,

your windows based calculator DOES have the square function. try clicking on view (from the menu) then selecting "Scientific".

johnnytheprickPost author@dr9106, he talks to fast.

megadroidnblastoidsPost authorhahaha i hate being rushed:D!!

james sumandoPost authorit help me for my physics exam!

JohnTrinhArtPost authori hate a physics test tomorrow and this is amazing review. thank you! 🙂

secretoppPost authorI didn't know about gravity … Then I took an apple to the head.

Matt KPost authorcheck out my science project for newtons laws on my channel tell me if its right or wrong

Vahe MirzoyanPost authorur videos are awesome but PLZ FOR THE LOVE OF GOD upload at least 360p

chronic tonicPost authorin the absense of air, would a feather fall slower or faster then a hammer? answer me that.

ZinzTheUprisingPost authordude how did u get so good in math im in pre alg. and i want to know im tryin to find a cure for cancer and learn this but how did you

StijnHmrAwesomePost authorBegining: that's no longer a mystery, it's because of the Higgs Field and the Higgs Boson as a force carrier. Awesome!

Thomas MellinPost authorDear Sal,

switch to Mac soon and get real rpn calculators to work with.

Will MadiganPost authoris sal fat?

jjojjorgePost authorGreat that the instructor stated that Gravity is "not well understood", because gravity is a mere effect, not a law. It appears that it is a law because because said effect can be computed, for example, from a classical-physics frame, or from the space-time. In any case, the real laws, and eventually a main law is what gives the apparent law of gravity.

The GabenPost authorcan can can it it it

Achebe IkechukwuPost authorthe units of force is not M/s2 thats acceleration.

TheSawJigsawPost authorDid anyone actually proved that gravity exist?

Maria SophiaPost authorಠ_ಠ

TheMightyWillPost authorwtf? O.o

thedude isthedudePost author9 now and they failed their tests

Nastascia BrownPost authorThere are more recent video with HD. The earlier ones are of poor quality but just as helpful (y)

Nastascia BrownPost authorMake that 9

TriturabisPost authoryour talking about the theory not the law right?

a law is an observation with an explanation as i understand it

PragyanPost authorgood video but you explain too fast.

kevin morenoPost authorthanks bro this helped me out now i gett it…

_Post authorLiek dis if you cri evertim.

nessay10Post authorwhy are there subtitles?

Nawreez HubailPost authorCool !!!!

Aishwarya BhattacharyaPost authorObviously!! Dis bloody is gud 🙂 lolz

omkar BhatnagarPost authorNice explaination

SUBIN.spockPost authorDFGHIPJHPÈËÁÊﬂÂ‡ﬁ‰›„ﬁÍﬂÎ‡ﬁÈÏ∏Ê·Á‚°”Ë·IJOP

ABCABCPost authorThank you for the helpful video. If you've got a Kindle, I recommend checking out "Great Formulas Explained" by Bektas. It's got a nice popular science section on gravity and orbits.

Chaoyan YuPost authorSAL IS AWESOME

Harshit PandeyPost authorLol I dont want to reveal my mass in this video!!

momen roshdyPost authorwhy r^2 ?? not just r ?

Grant PetersonPost authoromg these old videos

王雨生Post authorit is not very hard to understand.

prova akhtarPost authorAccording to newton's second law of motion F=ma

Here 'a' can be acceleration due to gravity

So , we can also write that ,F=mg

Or, g =F-m….(1)

And according to newtons law of gravitational force,g=GM.m/d2…(2)

Would you please explain the difference between these two formula….

AerosciencePost authorI would love a khan academy video on general relativity

Sven SvenssonPost authorWhy is is moon gravity lower then? mass is less so is the volume….

fnpPost authorcan someone help me? What are the factors that affect G? is temperature one of them?

Francisco LaraPost authorThank you so much bro 😀

Christine TaoPost authorIt must be distracting to try to explain and write and the same time. Mabye u can add/edit the voice in later

Vir Surya IrcasPost authorWill this 9.8m/s^2 change for a leaf which is flying freely in the air..?

TrowbloodPost author"Universal gravitation"… they said

Menreet GergesPost authorhow to solve this question

if the distance between the centres of two identical balls is 1 metres and the force of Attraction between them is 1 newton the mass of each one of them equals

Neil HelgesonPost authorMan, WHERE was this video when I needed it?!

Thanks for producing this.

sumit kumarPost authorMy new PHYSICS SOLVING APP.More then 150+ formulas,Solves for any variable you want,Covers up all physics.download now.https://play.google.com/store/apps/details?id=com.physics.lenovo.myapplication

RachelPost authorIn my textbook G=6.67 x 10^-11 m ^2/ kg^2, not m^3

Drive_A_PriusPost authorThanks so much. My physics teacher at school was so vague when it came to how to use the equation for Newton`s Law of Universal Gravitation. Your video helped me out a bunch!

Sara GarciaPost authorhow come the three feet was not added

Brooklynn BuffaPost authorWhen I still don't understand physics after watching these videos, I've accepted that there is no hope for me

Alamdar MehdiPost author2:03 wat just happened? xD

DivologyPost authorI'm Sal. I can do this job. I won't fail like all my previous jobs. I'm not a bartender anymore. I'm Sal.

Taha SilatPost author"And I don't feel like revealing my mass in this video so I'll just leave it as a variable"

Lol

Anshul PurandarePost authorSir which app do you use to make the videos ?

Rhino EDUPost authori was just searching about gravity and idk how i came across to this

Tadeusz PicaultPost authorI'm french

Josué GutiérrezPost authorWhat about your height, aren't you going to include it with your radius of the earth?

metal9lover9maniacPost authorC'mon man, you could have just used someone else's name for the mass.

Amrutha patrePost authorWhy is the distance squared?

JusticeOfAllGodZPost authorOlder than me

Rekha MaliPost authorNice

Umme YusufPost authorSal is funny: "I don't feel like revealing my mass in this video."

Halil SultanmamedovPost authorMass of Sal confused everything 😂😂😂

Guerras LawsPost authorQuestion. Has anyone thought of replacing

"F" for applied Force with "E" for applied Energy? Eg vs Fg?

Would that work? If we were to know how strong or weak the “gravity” is, then

we would know how much energy is being applied from within a planet or black

hole. Cause, without energy there is no gravity, magnetism, fields, waves,

motion, etc. After all, Force does not exist "physically" in the same

way that an object with mass does. "Force", as we know it, turns out

to be nothing more than an expression to express an idea like one would use the

word "Love" to express one's feelings. Meaning, Force or Net Force

does not push, pull or work for that matter.