# 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.

what is astronomy
The Study Of Celestial Bodies.....
simple branch of science which includes study of space and and its existed bodies
BHAVAN
so do I have to read openstax
if time is an illusion how can it be a true unit of measurement? so when time is not a true measurement space time and spacetime and position cant be a true measurement? so does everything can differs by the point of view? so nothing is absolute? what connects all if them? and where does theycomefro
BHAVAN
Nothing is absolute, all time measurements are relative. Think Einstein.
Mymp
then does the nature of the universe is not absolte?
BHAVAN
There's inatiquate information and data to determine these things as of yet and there by is a great need for farther exploration of the solar system, Galaxy and universe.
Mymp
what relates everything inthe space ? time or the expasion of our mind
BHAVAN
Time is a human derived measurement for relative measurements of things. Time is a byproduct of the human and the expansion of the mind.
Mymp
BHAVAN
Nothing is absolute. On the other hand of time, It seems that the fabric of space is absolute but is not. This is due to our limitation of our perception to the universe (itself). Speaking of limitation, we are enclosed in our 3 dimensional universe but the universe apparently looks like a 2
Jomari
2 dimensional object. My point is that the word absolute in this world is just the world absolute. Every element of what we know about the universe, such as space, time, and gravity, changes per dimension. So our laws of physics here, in my theory is just governed by our 3 dimensional matrix.
Jomari
How is this to be proven? Can this adequatly be proven with just the current amount of information and data.
Mymp
Mathematically speaking, we can come up to an infinite number of dimensions but then again our mind can only perceive this one we have and living right now. On my point of gravity, gravity exists because our universe expands. As it expands, it is accelerating and since gravity IS acceleration....
Jomari
... Hence, it exists. Thats why gravity isnt observed in the very early stages of our universe because it doesnt yet expands. Another topic is the time travelling. Indeed time is just an illusion. Our brain just perceives the collection of thoughts from our surroundings and made it organize by the
Jomari
This is what I mean though, it can be proven via math but not really via being done. Not yet. Not enough information and data.
Mymp
BHAVAN
does it have acceleration for gravity
BHAVAN
by the mind and create some kind of connections every "second" (or i should say points). This create the notion of time to make connections from what had happen to what is happening and what will happen. (This notion makes us more intelligent than other animals in the planet). Our notion of time is
Jomari
This is also what I have been saying, need to see with our own eye and get lots of data on these things to see for absolute sure if they do what we think they do, or if something else is happening and what and why. Right now it is no more than educated guess.
Mymp
is just pinpointing the possibilities in some point of space. So the term time travel is somehow technically wrong. Since time is just an illusion, and you woudnt want to travel to some kind of illusion would ya? It should be "possibility travel". Lets say it is possible to travel fourth...
Jomari
How would you set this up, what factors would be involved?
Mymp
i have a doubt about alien communication
BHAVAN
Since our dimension is accelerating to nowhere(hope we unify forces for more infos and data) blackholes are litterally holes that remain still from that point of time and space theyve been born.
Jomari
Mymp
Aliens are real, we are one of them. We are the proof it exist. We are just "aliens" to what we refer as aliens. We are also an alien race to them. So if we happen to communicate them, let be our first words to them are We are Humans in a way they can decode it that we are "humans". Humans that have
Jomari
have bad history but strive for the better.
Jomari
How would this be done
Mymp
Through vibration
Jomari
Explain
Mymp
Calibration of technology in a manner they can receive this encoded messages through vibration. Speaking of calibration, we dont have the "information and data" YET of these technology like the one we see in movies that simply translates messages. Yes we do have one, commercially available. The goo
Jomari
The google translator device, but it is for humans... how abour for extraterrestrial life, right? So what can we do now is to send thousands of thousand of different kinds of vibration from thousands of thousands of tries of calibrating these technology. Hey what technology? As of today,
Jomari
The mother of all invention is NEED. The value of the use and thereby the need has not arrived yet.
Mymp
what is the important of studying the astronomy?
its important because its great to study the unknown
Tankia
We need to study astronomy because of all the benefits to humanity, and all things both here on this planet and beyond. The more we know, the better it will be for the survival of the human race. We also need to expand the scope and human inhabitants elsewhere in the solar system and Galaxy.
Mymp
true very true it's a perfect answer according to me @mymp gem
Apeksha
well written
Tankia
I'm not even a bachelor degree, let alone higher. I am just a Associate of Science in Earth and Environmental science. I am also dyslexic.
Mymp
cool! 👍
Apeksha
cool! 👍
Apeksha
cool!!*
Apeksha
sorry typos!
Apeksha
what fascinated you all to be intrested in space
Tankia
space itself is fascinating wat more does it require to fascinate us
Apeksha
Has anyone ever wondered if any of the moons on either Saturn or Jupiter could be a viable place to colonize or what about our nearest Galaxy Andromeda. Anybody ever wondered if we humans could live there or if any other life is out there. Talk of colonizing Mars is already in the works.
Mymp
well I have on titan
Apeksha
yes it is but what really got me so fascinated was the vast life it holds of different living being its awesome
Tankia
hey wait I had replied to mymp gem saying I have wondered abt titan
Apeksha
but I can't c my dat reply only
Apeksha
ya so Titan and Enceladus r one of possible moons of Saturn and Jupiter where we have chances of colonizing
Apeksha
Titan has mostly hydrocarbons present over der and nitrogen I guess is in more amount
Apeksha
Great, this is the first step in creating a need, as need is the mother of all invention. This need goes along with the other factor which is an overwhelming curiosity of what's out there.
Mymp
The overwhelming common sense of having all the billions of galexies, stars and planets in the solar systems defys logic to think that we humans are the only life form in the universe.
Mymp
sun most important solar system and earth sun 7crore ton hydrogen Nd 6crore 95lakh ton hilium Nd gamma5lakh ton Jo ki hamesha Surya kirno badal rahi hai
ashish
we can actually use the hydrocarbons from Titan to make plastic through polymerisation and use it building purpose I mean colonizing purpose
Apeksha
and energy also we can extract through tidal waves caused in those methane seas by tidal energy and also der is high tides caused on titan
Apeksha
Does anyone here get Space News? If so, there's an interesting article on killer waves from Juniper that could destroy space craft. Other articles just as interesting too. these are real world issues that need to be addressed and overcome if we are going to be successful in interplanetary travel.
Mymp
yeah I get space news through emails from astronomy now but I haven't read abt dat btw could tell me the site from which you have got that?
Apeksha
what would happen if an asteroid hit the moon. how would it affect the earth?
there have been number of asteroids fall into the moon, it would have different effect to the moon than to earth, cause as i know, the crust of the moon is more rigid than earth. so it will just create a crater. but it will not affect the earth. correct me if im wrong.
dinda
Which matter found in the sun most..?
I think the hidrogen
Gúñjañ
the matter present in the sun is Plasma and the energy created within it due to nuclear fusion hear the hydrogen atoms fuses together due to high temperature and form helium atoms
Ummar
Helium and plasma
PALANI
hydrogen most temperature
ashish
hydrogen, the result of hydrogen fusion is helium, so as the star actively with high temperature fuse their hydrogen then they will emit high energy of light wave
dinda
I would like to say that Jupiter now has at least 79 moons as of July 2017.
Correction: 2018, not 2017. Sorry about that.
Dũng
do you all have interest in going to school for planetary science
yah why not
Gúñjañ
yesss but i don't how to go after graduation ? if anyone can guide me
Udit
after graduation... go through different exams like...JEST, GATE, TIFR, JAM to get into MSc Astrophysics or Astronomy
Shubham
mSc Astrophysics is where in India
Udit
IIST HRI IIT Indore MSc Astronomy Astrophysics specialization:- Pondichery University Tezpur University Bangalore University Hyderabad University
Shubham
thnks 😊😊
Udit
ok
Anshita
Or join Coursera. It has topics on Astronomy.
Dũng
do we need to pay money to join coursera?
Apeksha
actually we can also do msc in astronomy @ iisc banglore provided it's not integrated course as such😅
Apeksha
I don't think .it's free
Gúñjañ
humm k but there was an option on dat site saying sign in for free or something like dat so I have sign in and at the second step of it lets c wat happens next
Apeksha
ya..IISC also has MSc Astronomy
Shubham
what a quasar actually is?
quasar is an unusually bright object found in the remote area of the universe
What cause it?
sanskriti
The reason for this is unknown because the barriers are too far away and too small. But according to a theory, matter drawn from black hole, light and energy are emitted from the object called quasar, so it is said that the quasars are very bright
Burak
Burak
Eath is Blue marzble
what is the triad of Venus
Will you able to discuss what is in the astronomy as a whole?
from the beginning of astronomy 'til the present.
Joecy
till the fate of the universe
Kevin
till the universe expanding
Mr
please discuss it to me because it's hard for me to get reliable discussion of it
Joecy
hello joecy well Astronomy is not small to discuss? what do you want To discuss?
Mr
btw we humans first ever recorded counting system and math was based on only 4fingers on the left hand using the left thumb to count the knuckles on 9 digits dating back to Sumerian times
KATASHA
what about a pre-main sequence star. I thought those stars were different from protostar - a type of T Taurie?
Jeffrey
How can we differentiate between space itself expanding and the stuff within space expanding?
Hello JAKE Astronomers predict that Dark energy is the reason of expansion.Think of the universe as a giant balloon. If you mark multiple points on the balloon, then blow it up, you would note that each point is moving away from all of the others. Universe is expanding from everywhere
Mr
Lol is this a trick question? you can see the obviously basic of things when it's the "stuff within space" is expanding the "stuff" expands individually and completely separate to space itself which is the 'container' for lack of a better word for all "space stuff" Easily discernable either way
KATASHA
The fact that space itself has a finite volume and is expanding is counter intuitive and therefore in principle beyond our imagination. that objects within this finite space are expanding, for example whe xou blow up a balloon is immediately intelligible.
Drafi
It can easily be seen and measured.
Drafi
When we speak of the expanding space, we automatically imagine some kind of voluminous object like a balloon. The term "expansion" itself implies that there is some space, into which the expanding object expands.
Drafi
However, this is not so in the case of the expanding universe. It does not "expand" into some existing space, because it IS space itself. Therefore, the term "expansion" used in connection with the universe is misleading.
Drafi
Ultimately, we have to come to terms with the fact that we live in a world, which is not intelligible on the basis of our personal experience and imagination, but can only be described mathematically. The wonderful and mysterious thing is, however, that these counter intuitive mathematical theories
Drafi
have consequences that can readily be seen and felt and understood.
Drafi
A kind of paradoxical situation, isn't it?
Drafi
The answer to your question, Jake, is therefore something like: The expansion of stuff within space can be seen directly, measured and understood. That is, we can access it intuitively. The expansion of space itself can also be measured as well as explained by mathematical-physsical theories.
Drafi
It can even be seen, albeit only by observing the movement of the galaxies, because in an expanding space their mutual distance increases. Only grasp the whole picture with our imagination we cannot.
Drafi
I dont have a lot of knowledge but let me ask a question None of any satellite has left The milky way galaxy so how did they created the model of the galaxy as they can't see it ? we can understand that we can see other galaxies by telescope but how we were able to see the Milky way galaxy ?
Priyanshu
priyanshu Yep you are right but there are many other galaxies outside our Milky way . Astronomers have observed their positions and behaviors and In the Milky way Astronomers had created the Milky way model by tracking the positions of other stars and their distance and behaviors
Mr
and what is the relation between the universe's expansion and dark matter
Gúñjañ
Gja Rm well Astronomers didn't know that What is actualy Dark Matter but Theory says that our universe is made up of 80%of Dark Matter and about a quarter of its total energy density
Mr
why does the universe expands because the law of conservation of energy says that energy can't be created so by expanding the space is expanding as translational energy and from where this new matter of space is coming for expansion of universe.
Priyanshu
ok what I am trying to say is :where the universe expand ?
Gúñjañ
GÃºÃ±jaÃ±. Think of the universe as a giant balloon. If you mark multiple points on the balloon, then blow it up, you would note that each point is moving away from all of the others. Universe is expanding from everywhere
Mr
priyanshu Let me tell you if the critical density would be more than the actual density of the universe the universe will be expanding forever but if the critical density is less than the actual density then the universe will collapse
Mr
Mr astronomer yah but the ballon expand in its air .do you think that the universe has some things whitch it expand?
Gúñjañ
yep Gja Rm Scientist did measured a crital density of the universe if the critical density would be more than the actual density then the universe will be expanding forever but if the critical density would be less than the actual density then the universe will collide better known as big cruch
Mr
Why does a Neutron star know as the strongest magnet in the universe instead of a Black hole?
that would be a magnetar- a type of neutron star just like pulsars but with very high B fields.
Kevin
Kevin What is b field? PLEASE could you explain
Mr
what is the cause of blackhole
a collapsed massive star
donot
A dead star with intense gravity
Saaketh
star collapse remnant greater than 1.4 solar masses
Kevin
The Chandrasekhar Limit = 1.4 Solar Masses.....
when a massive star collides Under it's own weight
Mr
when a massive star is run out of fuel to do its activities and the gravity force blow it up
dinda
Gúñjañ
a wormhole or whitehole is predicted to occur naturally or artificially, when two distant entangled black holes are pulled apart, they will form a shortcut that has two ends. help us to travel through universe and time.
dinda
but its is not yet proven, it is just mathematically possible
dinda
The Chandrasekhar Limit is the lower limit to a neutron star. The upper limit is approximately 3 masses. Bear in mind that the initial mass must be substantially larger, as much of the mass is lost in the expansion and explosion. It is the core that forms the neutron star or black hole.
Gary
what is the difference between An Astronomer and a Cosmologist?
cosmologist only learn cosmology right. an astronomer is learn all about astronomy, including cosmology
donot
Cosmology Is The Study Of The Universe As A Whole, Origin And Development Of The Universe.....
astronomy include cosmology, astrophysics, astrodynamic and astrometry
donot