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

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

## 100 thoughts on “Introduction to Newton’s law of gravitation | Physics | Khan Academy”

• ### dr9106 Post author

you 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.

• ### dr9106 Post author

o 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 Philimeter Post author

You don't want to disclose your mass…wow…just wow.

• ### Magicman Post 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 >.>

• ### Magicman Post 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 Mark Post author

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

• ### Kosekans Post author

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

• ### Annie Armstrong Post author

u 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?? 🙂

• ### divvy1400yam600 Post author

You 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 Tkachuk Post 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.

• ### divvy1400yam600 Post author

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

• ### divvy1400yam600 Post 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 Tkachuk Post 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 Waffles Post author

umm what happened to your height why didnt you add that in the distance?3m?

• ### Chicken and Waffles Post author

thanks a lot though this really helps me out1!!!:)

• ### Amber Lawson Post author

all this was was a bunch of math equations! what the heck! i am solemnly disappionted!

• ### Raf Uzi Post author

great video sal..thanx

• ### Jonathan Palmer Post author

this 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.

• ### Ambriz745 Post author

Great work. Thanks!

• ### lupischuckle Post author

This 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!!

• ### LiamOHorrible Post author

great 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…

• ### Lilgabbyj Post author

I love how you change colours to keep it interesting =)

• ### Minky Tres-vain Post author

Thank you. So, so much.

• ### narpup Post author

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

• ### B1indfire Post author

Sal, 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.

• ### Kanbei Post author

How does it feel to be able to cancel your mass?

• ### Christophe Valahu Post author

Sorry 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.

• ### supermanuman95 Post author

my 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 Cocabo Post 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 Suarez Post author

A 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 gaona Post author

so would this some what prove that levitation is not possible?

• ### Chantheman5 Post author

woah 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.

• ### Chantheman5 Post author

6 retards disliked this

• ### SSuperCuriouss Post author

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

• ### johnnytheprick Post 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".

• ### johnnytheprick Post author

@dr9106, he talks to fast.

hahaha i hate being rushed:D!!

• ### james sumando Post author

it help me for my physics exam!

• ### JohnTrinhArt Post author

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

• ### secretopp Post author

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

• ### Matt K Post author

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

• ### Vahe Mirzoyan Post author

ur videos are awesome but PLZ FOR THE LOVE OF GOD upload at least 360p

• ### chronic tonic Post author

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

• ### ZinzTheUprising Post author

dude 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

• ### StijnHmrAwesome Post author

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

• ### Thomas Mellin Post author

Dear Sal,

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

is sal fat?

• ### jjojjorge Post author

Great 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 Gaben Post author

can can can it it it

• ### Achebe Ikechukwu Post author

the units of force is not M/s2 thats acceleration.

• ### TheSawJigsaw Post author

Did anyone actually proved that gravity exist?

ಠ_ಠ

wtf? O.o

• ### thedude isthedude Post author

9 now and they failed their tests

• ### Nastascia Brown Post author

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

Make that 9

• ### Triturabis Post author

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

• ### Pragyan Post author

good video but you explain too fast.

• ### kevin moreno Post author

thanks bro this helped me out now i gett it…

• ### _ Post author

Liek dis if you cri evertim.

• ### nessay10 Post author

why are there subtitles?

Cool !!!!

• ### Aishwarya Bhattacharya Post author

Obviously!! Dis bloody is gud 🙂 lolz

• ### omkar Bhatnagar Post author

Nice explaination

• ### SUBIN.spock Post author

DFGHIPJHPÈËÁÊﬂÂ‡ﬁ‰›„ﬁÍﬂÎ‡ﬁÈÏ∏Ê·Á‚°”Ë·IJOP

• ### ABCABC Post author

Thank 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 Yu Post author

SAL IS AWESOME

• ### Harshit Pandey Post author

Lol I dont want to reveal my mass in this video!!

• ### momen roshdy Post author

why r^2 ?? not just r ?

• ### Grant Peterson Post author

omg these old videos

• ### 王雨生 Post author

it is not very hard to understand.

• ### prova akhtar Post author

According 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….

• ### Aeroscience Post author

I would love a khan academy video on general relativity

• ### Sven Svensson Post author

Why is is moon gravity lower then? mass is less so is the volume….

• ### fnp Post author

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

• ### Francisco Lara Post author

Thank you so much bro 😀

• ### Christine Tao Post author

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

• ### Vir Surya Ircas Post author

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

• ### Trowblood Post author

"Universal gravitation"… they said

• ### Menreet Gerges Post author

how 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 Helgeson Post author

Thanks for producing this.

• ### sumit kumar Post author

My 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

• ### Rachel Post author

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

• ### Drive_A_Prius Post author

Thanks 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 Garcia Post author

how come the three feet was not added

• ### Brooklynn Buffa Post author

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

• ### Alamdar Mehdi Post author

2:03 wat just happened? xD

• ### Divology Post author

I'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 Silat Post author

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

• ### Anshul Purandare Post author

Sir which app do you use to make the videos ?

• ### Rhino EDU Post author

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

I'm french

• ### metal9lover9maniac Post author

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

• ### Amrutha patre Post author

Why is the distance squared?

• ### JusticeOfAllGodZ Post author

Older than me

Nice

• ### Umme Yusuf Post author

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

• ### Halil Sultanmamedov Post author

Mass of Sal confused everything 😂😂😂

• ### Guerras Laws Post author

Question. 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.