# 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.)

## 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?

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.

#### Questions & Answers

In need to read some books about Astronomy so how can in get it actually leg live in Ethiopia can uh help me with that?
I am sri Sharan .m .what is my best favourable numbers
how can we know it
sruthi
😂😂
Rango
bahut hard
Rango
Why no object can travel with speed greater than light?
Because the mass of light particles is zero
Asim
Can mass be negative?
geometry
No
Asim
anybody stated that the light is the only thing is speed
sruthi
geometry are you a korean or kpop fan
sruthi
in this universe anything can be faster than light because we simply can't get to an conclusion
sruthi
I am a an Army but lets not bring spam here.
geometry
But why mass can't be negative. What I mean is how can we claim an object made of strange matter has positive mass. In other words, theoretically can negative mass exist?
geometry
in our observable universe nothing is faster than the speed of light
Rango
Thanks
geometry
But theoretically, is it possible? Sorry I'm being very curious..
geometry
I don't know about dark matter but may be you should think about dark matter because dark matter are really strange
Rango
Exactly so theoretically, an dark matter lazer can be greater in speed. Also maybe quartz..
geometry
may be but i am not sure about quartz and btw techyons travel faster than light but techyons are hypothesized
Rango
there are many objects which are perceived to be faster than light
Ganeshan
The object have their own declination rate in speed,the air friction can develop higher temperature resulting the object to be disappear in molecules,not considering the Physical conditions in space.The object should be unaffected with the air friction and also speed should proportionate with fuel.
Near
what is Deja Vu theory?
Have you ever felt like something has ever happened before? That's Deja Vu. The Deja Vu theory says that once you have those visions, you are actually experiencing what an alternate reality would have been. Basically it's the collision of both our universe and another.
AlteredEdge
Yeah it gives us an idea about the existence of a parallel universe
Debabrata
is this a hypothesis? or theory? isn't there something with your brain/memory processing the image or info twice in a few seconds?
Collins
I do also love this experience, seems so unreal but real all at once.
Collins
this can be real if we will solve the mystery of quantum physics .
YOG
I was giving just giving my own hypothesis of the general topic. While it would be interesting to find that we transitioned through dimensions, I think it just boils down to a heightened ability to predict future outcomes and a series of subconscious decisions to enact one of those possible outcomes
AlteredEdge
What I'm saying is that it's all in your head. 😂
AlteredEdge
yeah its all in our heads for sure, the brain is amazing, all of the above hypothesis really interesting. one day hopefully we might figure it out.
Collins
I hope that this hypothesis might be proved true
Debabrata
I feel deja vu is kind of a wormhole which connects us to a parallel universe.
geometry
I like what you said 'alterededge' "dena vu" is a vision of a past memory reenacting itself at an unexpected time and place. traveling and transitioning through dimensions.
Alba
opps, "deja vu"***
Alba
you are are right Geometry Lover.
Alba
Deja vu might even prove the existence of future time travel.
geometry
Well I'm not exactly saying it's a memory, it still hasn't happened yet, more like subconscious pre-cognitive thinking, where your mind eventually leads you down a path that makes the "deja vu" experience reality true after you had it.
AlteredEdge
We says time as a 3rd dimension and space as a fourth dim, so as come to 5 dimension what we say? I hope you got my point
Asim
According to string theory there are 10 dimensions
Debabrata
Yes you are right Mishra
Asim
But Tesseract is said to be 5 dim
Asim
How?
Asim
How do giants planets remain gaseous when they are located in cold regions of the solar system? Do they generate enough heat and if they do, are they not able to also heat their moons?
Kuda
Kuda just to answer part of your question. The gas inside Saturn for example is extremely dense not like gas in a room. The definition of gas is that the particles have little to no interaction between each other meaning there's no chemical bonds.
Sandra
hello ,what kind of question is that?
what is weather
Hey guys, question. It is said that Uranus' famous axial tilt of 98 degrees was caused by collisions billions of years ago. How can a celestial body/object 'collide' with a body (Uranus) which is made up of gas and has no surface?
Although Uranus has no phyiscal surface, it still has a core. It's possible that in the early stages of the solar system, a rouge planet or moon tore through the upper levels of the atmosphere and was able to penetrate the lower cloud levels and eventually reach gas giant's core.
AlteredEdge
are there aliens in the universe?
might be possible but there is no true evidence of it.we can only assume because we don't know the exact size of universe,it's infinite,so possibilities always shown is in infinite.
Near
might be possible because UFO's are being seen on earth
Vinay
is also a little ridiculous
Tracy
I feel I need to confess the only life the universe created for us to see and feel is the one in human form on Earth. its possible we make ourselves sick straining our thoughts to think of connecting with human life on or in any other realm other than the one we are in.
Alba
goodnight, I will continue our conversation tomorrow.
Alba
there was nothing created for anyone, its literally just there, there is no reason, it just is, don't be dumb
Tracy
We Are Not Special, We Just Happen To Be The Species That Evolution Has Shaped So Far.....
If the universe is limitless, life could be limitless as well. According to science and mathematics of course!
stijn
how?
Emilya
The universe is so vast and complicated it's impossible to ever rule out the possibility of intelligent life, but the gradual realization by human society is that we are not "special" in any given way. I recommend everyone here watch Issac Arthur on Youtube, he takes a look into the Fermi Paradox.
AlteredEdge
Thank You AlteredEdge, I Will Check It Out.....
Adam i have a question
Asim
Why does traveling at close to light speed or being near super dense objects cause time to dilate?
good question. time is only what we made it. the way light travels with and without gravity has always been a wonder to me.
Collins
What do you mean without gravity?
Andrew
I'm actually not sure, this might be a silly question but does gravity effect light in respect to time?
Collins
As you move faster the slower the time
Asim
yes , gravity can effect light you can take example of black holes .
YOG
yes this makes sense, so do we know what kindo of effect it has on time around a black hole?
Collins
Since a black hole has an extreme amount of mass compacted into such a tight density, it warps space and time around it. Why? The main reason is gravity. It is always the dominant factor in black holes. Light in this case is absorbed like everything else.
AlteredEdge
Time in a black hole is slowed down compared to outside the black hole, this again is caused by gravity. Same principle works on Earth.
AlteredEdge
but black holes only bends space-time febric and light didn't change its path it always travel in straight line but the space febric is curved so it looks like that light bend or obserbed by black holes.
YOG
Black Holes do bend the fabric of space-time, but light is no exception. Light is matter just like everything else.
AlteredEdge
this is great info/convo. without a black hole, does gravity effect light in any other way,? like the way water bends light. just curious if the knowledge is there, any site recommendations for research, would be greatly appreciated.
Collins
So like your saying, outside of the extreme of a black hole, light travels in a straight line. However when it comes in contact with a large mass (lets say the sun) it curves space around it. So from an outward appearance the light bends to the gravity which causes what we call gravitational lensing
AlteredEdge
yes exactly, ok wow yes that makes alot of sense, thank you very much for this info/feedback, gravity seems like the top of the food chain in the universe, trying to find out, for my own research, how much we know about it to date and its affect on other objects/masses etc. thanks again
Collins
Of course! Also to help you out incase you didn't already know, but gravity travels in waves and varies in strength.
AlteredEdge
wow ok I did not know that either, thank you,. slightly like the way sound travels maybe? other info I will be glad to hear if your sharing, thanks again AlteredEdge
Collins
what is the definitions of planet
A celestial body orbiting around a star
Asim
How to appear for MCQ in this app
I l don't understand questions
which quesrions?
Ankit
let it be
nitisha
How to make a telescope
Steve
***wikihow.com/Make-a-Telescope
Jennifer
optical mechanics
Astro
aptical
Nkateko
Why the God make universal ?
Trung
because God itself don't know.
Near
Which one has the ring
Saturn venue and even Jupiter all have rings the rings on Jupiter, however, aren't so easily noticed due to them only being viable through infrared
Hunter
visible *
Hunter
they each have three rings but not as you might think just think of them all as one big ring because that's basically what they are but they are desperate individual rings
Hunter
separate*
Hunter
can you tell me what is a quantam elighment? Lets see how many people give write answers
can you tell me what is a fomalhaut?
gdjm
Fomalhaut Is The Brightest Star In The Constalellation Of Piscis Austrinus.....
joe.
Tracy
Do You Mean Quantum Entanglement?
yes
gdjm
No Adam fomalhaut mean eye of universe
gdjm
quantum entanglement is when a husband has been married so long to his wife that he is directly influenced by her action usually in an opposite way. 🤣
Jocofranc
It Is Also The Brightest Star Of The The Constalellation Of Piscis Austrinus.....
who was the first person to get to the planet
Isaac
Is 5 dimensional exists
Asim
Hello
Asim
Hi, have u read about the many dimensions we possibly have? it's more than 5.
Collins
there are 11 dimensions acc. to the M theory, 10 acc. to string theory and 26 acc. to bosonic theory. but we basically follow the M theory ..
BHUMI
thanks for clearing that up.
Collins
Asim