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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.

Astronauts in free fall.

Photograph of four astronauts in free fall.
While in space, astronauts are falling freely, so they experience “weightlessness.” Clockwise from top left: Tracy Caldwell Dyson (NASA), Naoko Yamzaki (JAXA), Dorothy Metcalf-Lindenburger (NASA), and Stephanie Wilson (NASA). (credit: NASA)

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 = ( M 1 + M 2 ) × 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 = a 3 P 2

Since a = 1, a 3 = 1, so

M 1 = 1 P 2 = 1 0.71 2 = 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.)

Check your learning

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?

Answer:

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.

Got questions? Get instant answers now!

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 gravity = G 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.

Questions & Answers

what do people do when sleeping
Olivia Reply
people when sleep they actually shutdown there conscious brain but the subconscious brain is it still on so that is the reason why you see dreams and suddenly wake up when you feel thirsty
Amritansh
really?
rizza
how to control your emotions/feelings over special someone?
rizza
there is no such trick honey. you just gotta distract yourself with better things.
Suraksha
yup crct
Amritansh
and always remember that you are enough. you don't need somebody else to make you feel important and loved
Suraksha
are there really twenty four hours in a day
Olivia
I heard that there are 36 hrs in a day we just think there are 24
Olivia
hey I GUESS our home clocks show 24😂😂
Amritansh
hey suraksha I didn't get what you said about imporatnce
Amritansh
cool anyway what happens when a black hole dies
Olivia
it becomes a white hole
Subhash
really I thought it sucked up it's self
Olivia
How does a black whole die?
basim
black holes just evaporate overtime through a process called Hawking radiation
Subhash
when there is nothing left for it to suck up it eats it self then there is nothing in space anymore
Olivia
Amritansh what I meant was, that you are important even though others might not show it to be so. as an individual you are valued and important
Suraksha
why do peoke love
Olivia
people
Olivia
it's just a natural feeling of bondage as well as possession. we humans call it "love" because that makes us feel more connected rather than just saying it's because we can't function without one another
Suraksha
what are quasars
Amritansh Reply
what is siphon
pankaj Reply
what is mama radiation
Pragiti Reply
I GUESS YOU ARE asking gamma radiation so it's nothing but a type of radiation of light which is at very high frequency and is very dangerous for human beings usually when there is a generation of photon inside the core of the sun it emits a large amount of gamma waves.
Amritansh
the time for planet formation must vary with the luminosity of the star? Disks must last much longer around a M-dwarft? please explain how planet formation varies as a function of star luminosity.
Jeffrey Reply
what do you mean by light year
Prabha
A lightyear is an astronomical distance of 5.9 trillion miles.
James
a light year is the speed of light times the total amount of seconds in a year. distance in physics is speed x time, so a light year refers to the total distance the light travels in a year
Levis
thanks for helping me
Prabha
Explain the formation of a black hole?
Prabha
a black hole is formed when a star dies . usually when a star dies it looses all of its nuclear energy but has its gravitational pull which then acts as the gravity of the black hole . a black hole absorb all the light therefore looks black . if you have any other question ask
Amritansh
what is atoms
Suman Reply
atoms are the smallest partiles that make the whole universe.For a measurement. if an atom were the size of a ball......The ball would be size of the Earth.
Sangeet
the smallest unit of an universe but it is not true the smallest thing in universe is quarks
Pragiti
The smallest thing in the universe is the arrogance of scientists who think they are never wrong.
Loren
You mean the greatest?
Cyclone
i believe so
daniel
see I GUESS the smallest indivisible particle in the universe ARE the glucons and quarks
Amritansh
do we are alone in universe
ninja Reply
no not all it is said that in our milky way galaxy there are more 100 thousand planets like earth
Amritansh
is the astroid belt shaped like a torus? or like Saturn's disc?
Abhishek Reply
torus
ninja
torus
Robert
can i know deep about black hole
Monisha Reply
yupp ask questions about whatever you wanna know in black hole?
Paras
where does it lead
Vanessa
how black holes are detected in deep space as we are unable to see them.
jawad
if black holes are hypothetical then how do they detect them?
Alvis
who said blackholes are hypothetical?
Ehan
They are detected by their gravitational pull...
Ehan
also we can detect them by X-rays as they emit hawking radiation as they 'shrink'
Levis
hawking radiations are not detected yet...
Ehan
nopes that's not how you detect black holes. Gravity curves space, and light bends around heavy objects. Black holes have very very very high mass. So light bends so much that it cannot pass. When the light of the stars behind suddenly vanishes. => black hole is present in between us and that star.
Abhishek
see I think we detect the black holes by their surrounding because yes they bend space and time but the gases around them become so light that they start emitting visible light which our sattalites catch and we find them
Amritansh
and yes black holes aren't hypothetical
Amritansh
to find astronomical units do you divide or multiply?
Bethany Reply
I think it depends what you're converting from. i.e. from km you divide
Fab
I tried that for question a in section 0.3 but the answer doesn't seem right
Bethany
make sure you're using consistent units m/m
Fab
i too had the same doubt
Monisha
hi dear
jawad
can you tell me what is ecliptic ?
jawad
the great circle formed by the intersection of the plane of the earth's orbit with the celestial sphere; 
Monisha
OK thanks
jawad
who is the father of Astronomy?
subhajit Reply
Me ;)
daniel
I think Galileo
Prabha
Copernicus, Nicolaus.....
Adam
which telescope is best for beginners ?
jawad
Do You Want Low Maintenance Or High Maintenance Optics? Do You Want To Look At Solar System Objects Or Deep Space Objects? Or May Be You Want To Split Doubles, Do You Live In A Big City Or Suburbs?
Adam
I want low maintenance. I want to see deep Space objects. I live in big light polluted city.
jawad
sir I have Nikon 16*50 binocular but now I want to buy a telescope.
jawad
i have got money that i earn with i am a doctor that working at st.louis jewish Centre.i am very helpful for people that they need help with.
Asali
What's Your Budget?
Adam
Deep Space Objects Are Gonna Hard To Come By In A Light Polluted City..... So Far I Would Recommend 8 To 10 Inch Schmidt Cassegrain Telescope, For Deep Space Objects You Need Light Gathering Power, Now A Decent Scope Like What I Just Described Is Gonna Run You About $800 To $1000 Dollars.....
Adam
And That's Just The OTA, Optical Tube Assembly..... Then We Gotta Talk Mount And Tripod, And For Good Stable And Steady Views We Need About Another $1000 Dollars For Mount And Tripod.....
Adam
my budget is almost 1000 dollars.
jawad
my budget is almost $1156.00 dollars each years
Asali
big diameter and lenth are good, i got my first telescope for $300 and it works real well for planets.
daniel
if you want to do amature astrophotography, what you can do is mount a webcam or your phone to your telescope and have a tracking mount attached so you can look for different deep space objects and take pictures. I have a couple I did using this method
Mark
A Big Dobsonian Might Be In Order, But That Scope Is Very High Maintenance..... But For $1000 Dollars, You Can Get A Real Nice Dobsonian And They Perform Excellent On Deep Space Objects, The Darker Your Observing Location Is The Better.....
Adam
guys this is my first day of i arrived in the u.s i need your help guys what does telescope means
Asali
so, a telescope is a thing you look through to see things far awY
Mark
A Tool Used To Observe The Sky.....
Adam
thank you guys for you help me i appreciate with that i will always thank you guys
Asali
what does physiognomys mean?
Asali
what happen if earth stop to rotate?
Sijan Reply
well first of all we wouldn't have day and night and it would get cold in the dark side humans and animals would have to get use to the darkness. plant would not he able to grow on the dark side either. Ad for the light side or "day" its the same thing but just...hot.
Ghost
and contestant datlight such could be harmful beacuase of the constant if rays
Ghost
Our gravitational field would collapse.
Hannah
Magnetic field sry. That means no shielding from cosmic rays.
Hannah
actually we would have day and night...but each day would last a year. We would also still have a magnetosphere unless the Earth's core also stopped rotating. Gravity would increase as we would lose any centripetal effect. We would only have one tide per 29 days as the moon orbits us.
Joe
we would still have gravity Hannah because we would still have mass!
Joe
pretty sure there would be no more rain or wind because any warm air and water vapour would just rise and fall above wherever it came from.
Joe
As we are rotating right now, if the earth suddenly stopped, objects that are not bound to the ground will get flung due east at very high speeds. It would be very catastrophic. That's the first thing that'll happen if such an event were to happen.
Cave
if we stop rotating then there will be drastic changes in our environment for example as Joe said earlier that we will have gravity as we have mass but the moon will start disappearing for some time and then appears for a sudden and also we will stop encountering different changes in temperature
Amritansh
what is comets?
Ido Reply
the bottom of the page of chapter 13 thinking ahead describe it
Chelsea
I also don't know but I think it is star
Sijan
A comet is composed of small rocks and dust particles cemented together by frozen gas and ice.
shiela
and when the ice and the cold stuff on a comet heats up, by the sun as it closes by, some matter escape and we see a tail.
Abhishek
when any asteroid from the Asteroid belt or from outside comes towards us and it actually come at a hi speed or rather very high speed so it form a tail behind the main centre of the comet and it is said that it actually revolves around the sun
Amritansh
I once watched a show discussing finding dark matter ON planet earth, deep down inside caverns where sound and light are absent. I seem to remember them also saying that the slightest of sound would "charge" the matter up. If the solar system is primarily dark matter, could we use sound to travel?
Jamie Reply
I thought the same thing. If space is a vacuum and sound does not travel in a vacuum, it would be difficult?
James
What exactly is dark matter?
Sharadhi
from what i gathered, dark matter is incredibly motionless atoms. Almost dormant, and they are easily disturbed? i am by NO MEANS an expert on any of this. just a curious mind... if sound doesnt travel in a vacuum, maybe the light then? disturb the matter with light and maybe 'swim' it?
Jamie
yes, the sound can be converted as an electrical impulse, which can be converted to light. and if we can detect this light at the receiving end then we can convert it back to sound but only if a material medium is present for the sound to travel to our ears.
Abhishek
what are whitehole a wormholes
gajanan Reply
holes
xBeex
***en.m.wikipedia.org/wiki/White_hole ***en.m.wikipedia.org/wiki/Wormhole
xBeex
wormholes are those holes through which we can travel to past
ninja
in an theory of Black Hole it was said that black holes are the portal which you know pulls all the matter from the from the present universe and through a white hole or a warmer it gives out to an another universe but it is not really so that its true or not
Amritansh
how come people don't float all around the world
Olivia
why do black holes form
Olivia
black hole forms when a star dies actually what happens is that when a star die it releases all of its nuclear energy so the only thing that the star is left with is its gravitational pull so actually is that the star is left with the core which then becomes the Event Horizon of the black hole
Amritansh
cool but what happens when there is nothing left for the black hole to suck up
Olivia
yep it is a nice question C actually the quantity of anything in this universe is infinite so this case cannot happen but to answer your question I must say that to remove it's hunger the black hole Would Suck up itself
Amritansh
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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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