# 3.3 Newton’s universal law of gravitation  (Page 3/4)

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Newton’s law also implies that gravity never becomes zero. It quickly gets weaker with distance, but it continues to act to some degree no matter how far away you get. The pull of the Sun is stronger at Mercury than at Pluto, but it can be felt far beyond Pluto, where astronomers have good evidence that it continuously makes enormous numbers of smaller icy bodies move around huge orbits. And the Sun’s gravitational pull joins with the pull of billions of others stars to create the gravitational pull of our Milky Way Galaxy. That force, in turn, can make other smaller galaxies orbit around the Milky Way, and so on.

Why is it then, you may ask, that the astronauts aboard the Space Shuttle appear to have no gravitational forces acting on them when we see images on television of the astronauts and objects floating in the spacecraft? After all, the astronauts in the shuttle are only a few hundred kilometers above the surface of Earth, which is not a significant distance compared to the size of Earth, so gravity is certainly not a great deal weaker that much farther away. The astronauts feel “weightless” (meaning that they don’t feel the gravitational force acting on them) for the same reason that passengers in an elevator whose cable has broken or in an airplane whose engines no longer work feel weightless: they are falling ( [link] ). In the film Apollo 13 , the scenes in which the astronauts were “weightless” were actually filmed in a falling airplane. As you might imagine, the plane fell for only short periods before the engines engaged again.

When falling , they are in free fall and accelerate at the same rate as everything around them, including their spacecraft or a camera with which they are taking photographs of Earth. When doing so, astronauts experience no additional forces and therefore feel “weightless.” Unlike the falling elevator passengers, however, the astronauts are falling around Earth, not to Earth; as a result they will continue to fall and are said to be “in orbit” around Earth (see the next section for more about orbits).

## Orbital motion and mass

Kepler’s laws describe the orbits of the objects whose motions are described by Newton’s laws of motion and the law of gravity. Knowing that gravity is the force that attracts planets toward the Sun, however, allowed Newton to rethink Kepler’s third law. Recall that Kepler had found a relationship between the orbital period of a planet’s revolution and its distance from the Sun. But Newton’s formulation introduces the additional factor of the masses of the Sun ( M 1 ) and the planet ( M 2 ), both expressed in units of the Sun’s mass. Newton’s universal law of gravitation can be used to show mathematically that this relationship is actually

${a}^{3}=\left({M}_{1}+{M}_{2}\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{P}^{2}$

where a is the semimajor axis and P is the orbital period.

How did Kepler miss this factor? In units of the Sun’s mass, the mass of the Sun is 1, and in units of the Sun’s mass, the mass of a typical planet is a negligibly small factor. This means that the sum of the Sun’s mass and a planet’s mass, ( M 1 + M 2 ), is very, very close to 1. This makes Newton’s formula appear almost the same as Kepler’s; the tiny mass of the planets compared to the Sun is the reason that Kepler did not realize that both masses had to be included in the calculation. There are many situations in astronomy, however, in which we do need to include the two mass terms—for example, when two stars or two galaxies orbit each other.

Including the mass term allows us to use this formula in a new way. If we can measure the motions (distances and orbital periods) of objects acting under their mutual gravity, then the formula will permit us to deduce their masses. For example, we can calculate the mass of the Sun by using the distances and orbital periods of the planets, or the mass of Jupiter by noting the motions of its moons.

Indeed, Newton’s reformulation of Kepler’s third law is one of the most powerful concepts in astronomy. Our ability to deduce the masses of objects from their motions is key to understanding the nature and evolution of many astronomical bodies. We will use this law repeatedly throughout this text in calculations that range from the orbits of comets to the interactions of galaxies.

## Calculating the effects of gravity

A planet like Earth is found orbiting its star at a distance of 1 AU in 0.71 Earth-year. Can you use Newton’s version of Kepler’s third law to find the mass of the star? (Remember that compared to the mass of a star, the mass of an earthlike planet can be considered negligible.)

## Solution

In the formula a 3 = ( M 1 + M 2 ) × P 2 , the factor M 1 + M 2 would now be approximately equal to M 1 (the mass of the star), since the planet’s mass is so small by comparison. Then the formula becomes a 3 = M 1 × P 2 , and we can solve for M 1 :

${M}_{1}=\frac{{a}^{3}}{{P}^{2}}$

Since a = 1, a 3 = 1, so

${M}_{1}=\frac{1}{{P}^{2}}=\frac{1}{{0.71}^{2}}=\frac{1}{0.5}=2$

So the mass of the star is twice the mass of our Sun. (Remember that this way of expressing the law has units in terms of Earth and the Sun, so masses are expressed in units of the mass of our Sun.)

Suppose a star with twice the mass of our Sun had an earthlike planet that took 4 years to orbit the star. At what distance (semimajor axis) would this planet orbit its star?

Again, we can neglect the mass of the planet. So M 1 = 2 and P = 4 years. The formula is a 3 = M 1 × P 2 , so a 3 = 2 × 4 2 = 2 × 16 = 32. So a is the cube root of 32. To find this, you can just ask Google, “What is the cube root of 32?” and get the answer 3.2 AU.

## Key concepts and summary

Gravity, the attractive force between all masses, is what keeps the planets in orbit. Newton’s universal law of gravitation relates the gravitational force to mass and distance:

${F}_{\text{gravity}}=G\frac{{M}_{1}{M}_{2}}{{R}^{{}_{2}}}$

The force of gravity is what gives us our sense of weight. Unlike mass, which is constant, weight can vary depending on the force of gravity (or acceleration) you feel. When Kepler’s laws are reexamined in the light of Newton’s gravitational law, it becomes clear that the masses of both objects are important for the third law, which becomes a 3 = ( M 1 + M 2 ) × P 2 . Mutual gravitational effects permit us to calculate the masses of astronomical objects, from comets to galaxies.

My dear friends, can u plz tell me that among u guys who are in the field of cosmology
😢I am not there in cosmology
Samuel
Just A Science Fan.....
Samuel
I am also not in cosmology but I am just a fan or we can say science and part of NASA is my dream
Yoganshu
yoganshu Arya same here
Samuel
you are from which country
Yoganshu
hi yoganshu
Samuel
India
Samuel
which state
Samuel
I am also from India
Yoganshu
from delhi
Yoganshu
and u...?
Yoganshu
I am from Maharashtra
Samuel
from which state?
Yoganshu
You are a ASTRONOMER ...
Yoganshu
or a scientist..
Yoganshu
or just a member
Yoganshu
What is time...? not about Newton= time is constant..... that all scientists openions n point of view I m knowing. . what can be the Perfect Definition of Time
Who is the best astronomer of India at present time
Jayant Narlikar, Proponent Of Steady State Cosmology.....
What is the real colour of sun rays
white.. so white it becomes violet.. so violet it become ultraviolet
Tom
white and red and yellow
Bianca
Vibgyor
Samuel
the real colour of sunlight is White
the Sun's has a variety of waves all throughout the elextromagnetic spectrum.
Jacie
we only see it as a few bc of how some of them get redshifted (? can that term be applied for something so local?) by some particles in our upper atmosphere
Jacie
Vibgyor will be when, the white light will pass through the clouds ( prism ) then Refraction phenomenon leads us to 7 colours splitting from a single colour "White " light
so the sun rays r of White colour
Taurus in astronomy and horoscope?
how to put E=MC2
What Do You Mean By How To Put?
What Do You Mean By How To Put?
What Do You Mean By "How To Put E=MC2?
yep
Gospel
Hi guys
Samuel
i mean how NASA came to know the mass and diameters of Stars.how?
Gospel
how did they do using E=MC2
Gospel
thats my questioning
Gospel
that's easy formula's derivation
why all planets revolving orbits are nearly in equal inclination?
rishabh
dependent on the mass
no
Janak
I think because of the Suns gravity pull ,😕😕
Samuel
Samuel,. it's but obvious
what hubbel's law. and examples on it.?
Hubbel's Law is a Expanding Universe. The distant galaxies we see in all directions are moving away from the Earth, as evidenced by their red shifts. Hubble's law describes this expansion.
Роза
okk. sir/madam, i studied that all 3 laws.
Kavyanjali
i m solving examples on "p" square directly proportional to "a"cube
Kavyanjali
Evil space aliens drop you and your fellow astronomy student 1 km apart out in space, very far from any star or planet. Discuss the effects of gravity on each of you.
are you doing a test?
donot
can you give me details about how to solve problems on Hubbell's law
Kavyanjali
refer the Kepler's laws of planetary motion
use newton's gravity formula,i guess it will work
1412
if there is nothing else around I assume we would slowly fall into each other over a huge period of time for a cosmic high five. dam evil space Aliens!
Garrett
then we'd party.
Garrett
what is quantum physics
Quantum mechanic or physics is a branch of physics which deals with the dynamics of smallest things of all like atoms subatomic particles and elementary particles.
Ronaldo
Correct.....
Yes
ashish
what is circumstellar matter
Young T Tauri stars are surrounded by circumstellar disks, the material of  which coagulates into solid bodies within several ten million years as a first step for possible later planet formation. Most young stars are binaries or  multiple systems, and most binary T Tauri stars have separations of t
Burak
we were all circumstellar matter at some point =D
Garrett
where the Pluto has been gone
pluto hasnt gone,its stiĺl on kuiper belt with others
1412
it have not gone anywhere it is still present on it's position in kuipler belt
YOG
Pluto is present at its old postion in solar system.But now it is not in a list of planet because it is too much small in size so it is called as 'Dwarf Planet '.Now it is present on Kupier belt.
mrunal
Pluto is smaller then our moon. I like the new classification even though apparently it has been under constant dispute since the decision was made. keeps things clean. Planet clears it's orbit. Pluto is a dwarf planet.
Garrett
garrett is right on! Pluto doesn't have to do with size. it checks 2 of the 3 boxes needed to be a planet. the one missing is not clearing its orbital path.
josh
Correct Indeed.....
does anyone know the smallest thing in the whole universe I know I'm taking a general test
Quarks... Think so.. 🤔
Pavan
higgs Bo particle .. think so.
sakshi
higgs boson particle
sakshi
Andy
i guess andy should go and check his brain
Amritansh
God Particle is the smallest thing in whole universe.
mrunal
Quarks, Up,Down,Top, Bottom, Strange And Charm.....
is this some kind of channel for people who can't use Google?
Grisha
Who Knows?
atom
Gospel
No. You THINK that it is the smallest thing/particle in the universe, but that is only by the knowledge you & we have now. You cannot yet be sure of something being the smallest thing in the universe. Unless you have done some groundbreaking research of course ;)
Videos
thats my notion only
Gospel
of course string
Burak
mind
Moon
can anybody think that what is present before big bang?
I Don't Think Time Existed Before The Big Bang, So Talking About Anything Before The Big Bang Is Useless.....
but we have to think that what is present before big bang by which this whole universe is formed
YOG
because something can't create from nothing
YOG
it is thought by the scientists that 2 parallel universe collided with each other and got mixed in a point which exploded and formed the big bang It is thought that this process of big bang is continuous which means it will be repeated after a certain time interval
BHUMI
2 parallel universe collided with each other and got mixed in a point which exploded and formed the big bang, it is thought that this process of big bang is continuous which means it will be repeated after a certain time interval
BHUMI
before the big bang 2 parallel universe collided with each other
BHUMI
We Don't Know For Sure If That's The Case, We Need To Establish What Is Nothing?
One big crunch before big bang..just like now.. Our universe will end with big crunch or by expand.. More expand.. Much more since planets get separated 🖖 from its own core... I don't know more.. 😉
Pavan
how those two parallel universes came into existence
sakshi
no one knows what came before. The theory exists only because the numbers for expansion (calculated via redshift, measuring the CMB, etc) add up.
Jacie
We used to think that there were 3 possible endings to the universe - expanding , oscillating (cycle of crunch, then expand, the crunch again), and the steady-state theory (multiple places where matter enters the universe.
Jacie
However, the expanding model is the only valid one left. Dark energy and dark matter are speeding the process of expansion up exponentially. the process had been slowing down up till now. this means that there's no going back (or big crunch) and disproves the oscillating universe theory
Jacie
👍👍
Ashish
we also measured the density of objects and that is decreasing, meaning that all space objects (predominantly referring to galaxies) are moving farther away from each other. this means that the universe is not staying the same and disproves the steady-state theory.
Jacie
Oh yeah, and the steady-state theory stated that the universe has stayed the same and will not change Fun fact: the steady-state theory was first disproved when we discovered a quasar from really far away (meaning that the light reaching us was old and we saw into the past). It was so different
Jacie
and therefore disproved the theory
Jacie
Well Said.....
As for before the big bang, I find the application of entropy to a multiverse an interesting hypothesis. From the Law of Entropy, systems, left alone, will devolve to their least organized state. In the multiverse hypothesis, universes are popping in and out of existence all the time.
Damon
Time is relative, just frequency of events relative to other events. With no events, there is no time. If the big bang was an event that happened, then there must have been time before the big bang and something must have caused it to happen.
Toby
That's Pre Bang Physics, Strictly Speculation At This Point.....
Time is relative and critical to this question. As we don't really know what went before, we will need to make some assumptions. Before the big bang, I believe that there was dinner and a movie.....
Andy
before Big Bang there were matters and anti matters so this is a Theory of matters and anti matters it is believed that there was a battle between matter and antimatter in which matter won and that is certainly the reason that why we study States of matter all forms of matter
Amritansh
but if antimatter would have won what would be the nature of universe
sakshi
If Anti Matter Would've Won, The Universe Would've Look Exactly The Same As It Does Now.....
bc antimatter did win
Jacie
very slightly tho
Jacie
we can actually explain how universe came into existence by the theory of Quantum gravity. matter won over Anti matter because of neutrino there is present research going on neutrino or sterile neutrino it could be the answer I think once we find the cnu background radiation or cosmic neutrino bac
Ronaldo
I think that it's not possible to create anything from nothing so it makes a that someone or something was present which was beyond space and time it could be anything like even some thing which we humans will never explain I think that's beyond our thinking because we can think till infinity not be
Samuel
beyond infinity there was or is something that created or has control on all these things like infinity time travel and all stuff one thing that if time is not present than nothing can exists right
Samuel
So Who Created That SomeOne Or SomeThing That Was Present At The Time Of Creation? You Said That You Think It's Not Possible To Create Anything From Nothing.....
what dark matter do?
TARUN
We See Dark Matter's Effect On Regular Matter..... We Don't Know Much About Dark Matter, Except That It Interacts Regular Matter..... That's Why It's Called Dark.....
It Interacts With Regular Matter, Sorry For The Error.....
on my view thats the Christian holy bible is true on this reasoning,Genesis 1:1 says "in the beginning GOD created the Heavens and the Earth ".As we all know Something cannot come from nothing because its nothing,and nothing conclude it all that there is no matters at all.what do you all say?
Gospel
So Who Created God?
well, in my point of view, time was not even exist before the universe was created. we can say something is nothing because we live within something, and when we realize that there is emptyness within something, we say it's nothing.
dinda
no one and nothing created God, God creates everything.
dinda
Thats it GOD created everything in it,If we read the Bible it tells us all the evidence and Answers.In John 4:24 it tells us that GOD is a spirit.GOD is present everywhere.Thank u
Gospel
Didn't You Say That Something Can Not Come From Nothing?
Does That Include Your God? Or Are You Gonna Make A Special Case For God Coming From Nothing.....
God creates itself thats why we call God,and if He is not the creator of the universe then there will be no word "GOD"in every language in our universe
Gospel
If GOD doesnot exist then everything is permissible and not only permissible but point less...
Gospel
So Your God Came From Nothing?
So God Made This Astronmical Size Universe Just For This Little Blue Rock Floating Around An Average Star..... Sounds Like A Huge Waste Of Space..... And How Do You Know That A Planet Orbiting Proxima Centurai With Intelligent Life Use The Word God?
And The Bible Is Full Of Inaccuracies..... An All Knowing God Would Not Inspire A Book Full Of Incorrect Information.....
God created Universe conclude as we seen in the letter of Saint paul i.e in 1Korinth 13:9 said that like this"for we know in part,and we prophesy in part" conclude it all isn't it right.
Gospel
As mr Adam said before that is "Does that include your God? My answer will be like this=God didnot "include" HE IS ALREADY INCLUDED AS YOU HAVE SAID.
Gospel
And in another point as Albert Einstein quote that "God didnot create evil,just as darkness is the absence of light,evil is the absence of God".
Gospel
Anyway mr.Adam where are actually from? America? or where.....
Gospel
America, New York City..... Where Are You From?
my opinion is that only god can create something from nothing it seems confusing therefore I told it's impossible to think that how was everything created !!
Samuel
hello, m new to this group
deepak
I am from INDIA.
Gospel
Adam I told you that God is beyond our knowledge and understanding. and if your question is who created god ?then the answer is god was a self cause of himself {means god created him self by himself }it's confusing so the best thing is we shouldn't go beyond your knowledge
Samuel
I love America, cause many "world race teams"came to our place".I really wanna come.
Gospel
gospel hmar even I am INDIAN
Samuel
You Said That Can't Happen, You Are Making A Special Case For Your God..... God Was Created By Man, When Man Was Scared And Afraid And Wanted Answers..... That's Why He Has Human Attributes..... And Why Everyone Will See God Differently.....
i guess nobody has seen god, so it might be energy, the energy from the big bang, the ancient people might have realised that, but didn't know what to name it.
deepak
there is some sort of energy that is driving everything in this universe, people name it whatever they want, some crist, some brahma and some Allah.
deepak
and as samuel has said that god created himself, do we know where the energy for big bang came from
deepak
No one knows where the energy came from,where the matter came from,where the laws of gravity came from,where the Universe came from,where the space came from,where the big bang came from,where the galaxy,no one knows the exact answer so,my answer will be on Genesis 1:1 that GOD created itself.
Gospel
I have to jump in here a put in my 2 cents......Gospel, you stated that god made himself, I beleive Samuel made a similar statement. I am not saying you beliefs are wrong. Everyone can beleive what they want to, so i am making these statements to try to understand your beliefs. so with that in mind
josh
its just same as fundamental particles joined to form human and now the humans are studying and researching about fundamental particles.. this is same as fundamental particles are discovering themselves
deepak
there is a question why did god created himself?
deepak
How can you say something can't come from nothing correct ? But you can beleive that god created himself? You dont see a contradiction there? My other question would be, have you heard of the god of the gaps? Do you see the bible as evidence of you beleifs or a written account of %100 actuall events
josh
i am not a atheist.. i believe there is some form of energy that is responsible for our life and everything. but god has created himself might not be true. because how can something come out from nothing.
deepak
? Again i am just trying to understand your view not say your wrong or give you a hard time about what you believe.
josh
Man Created God.....
How do scientists feel the presence of dark matter?
saleha
when galileo was killed by church.. so they could do anything to make people believe that god came out of nowhere, god created the world and now the priests are his messengers. so they would do anything they want
deepak
How do scientists feel the presence of dark matter?
saleha
who knows, we might be experiment of some much more advanced civilization
deepak
there are endless possibilities
deepak
if you look in vedas you will find that religion is a way of living life in a particular way. name of god was imposed over religion just to control the crowd
deepak
Deepak , thats how I feel about this question and we cant prove either side of this coversations, there is no evidence that says god did it and we dont know what was here before the big bang, its all theories and inferences...... Best answer to original question, We dont know for sure!
josh
👍
Samuel
my last comment was a reaction to deepak's comment on endless possibilities of what could have been here.
josh
ya josh
Samuel
can we make quantum universe by quantum level bigg bang explosion.
what do u mean by quantum universe?
rutuja
see quantum mechanics is a theory like we use general relativity for the study and characteristics of big objects in the same way we use quantum mechanics for the small objects study. This is called quantum mechanics and the object or thing in the universe on which we apply it is quantum universe
BHUMI
string theory is more appropriate for universe
YOG
we all know that Albert Einstein equation E=MC2 is anyone know how to put this.
Gospel