Waste less time on Facebook — follow Brilliant.

Why earth has infinite strength?!!!

All massive objects, irrespective how much their mass is, got pulled to earth(or any other planet) at the same rate \((9.8 m/s^2\) on earth \()\) What is the reason behind this? all masses are pulled at the same rate... how? I searched in relativity... but no answer (the thing is that spacetime is curved can't explain it fully)

Note by Fahad Shihab
3 years, 11 months ago

No vote yet
6 votes


Sort by:

Top Newest

The thing is that inertial mass (the quantity that resists acceleration) and gravitational mass (the quantity that creates gravity) are the same (this is called the equivalence principle). So, the more massive an object is, the stronger its gravitational pull will be. At the same time, the more massive an object is, the harder it is to accelerate it. And these effects cancel each other out.

Let the force exerted on an object of mass \(m\) be \(F\).

That means \(F=\frac{GM_e \cdot m}{r^2}\) where \(M_e\) is the mass of the earth, \(G\) is the gravitational costant and \(r\) is the distance between the centers of gravity of the earth and that other object.

Let \(g\) be the acceleration that object experiences because of the gravitational force \(F\).

That would mean, \(F=mg\).

Get the two equations together and you have \(\frac{GM_e \cdot m}{r^2}=mg\).

The \(m\) in the left hand side of the equation is the gravitational mass (this is what creates gravity). And the \(m\) at the right hand side of the equation is the inertial mass (this is what resists acceleration). Turns out both of the \(m\)'s are equal and they cancel out.

So \(g\), the acceleration the object feels is independent of its mass (inertial or gravitational).

By the way, the curvature of spacetime perfectly explains why this happens. According to general relativity,masses cause a "curvature" of the spacetime, which we call as gravity, and that things move along the shortest path between two points in this curved spacetime. So, if nothing but gravity acts on something, it'll take the shortest route between two points. It doesn't matter how much mass that thing has. Its movement due to gravity is a property of the geometry of spacetime. It is completely independent of its mass.

Hope this helps! Mursalin Habib · 3 years, 11 months ago

Log in to reply

@Mursalin Habib again another question arises... why does spacetime curves around masses? is gravity having particles like light do? Fahad Shihab · 3 years, 11 months ago

Log in to reply

@Fahad Shihab


Brace yourself for the most unsatisfactory answer ever...

The universe acts in mysterious ways. There is no reason behind it. It is the just the way it is for no apparent reason. For example there is no darn reason for two bodies of mass to attract each other. It's weird! Why would they do such a thing? It doesn't make sense.

The universe is not supposed to make sense. Because the universe couldn't care less about what makes sense to us. It doesn't give a damn about what we find intuitive.

Special relativity seems really counter-intuitive to a beginner. Again why would the speed of light be the same to everyone no matter how fast they are moving? But remember that intuition is based on experience. Almost everything we interact with everyday is slower than 60mph [I haven't done a survey]. At the scales we’re used to the physical laws are quite intuitive. If we experienced close to \(c\) phenomena everyday, we'd find all the weird stuff like time dilation and length contraction very intuitive.

What I'm trying to say is when physical laws work actively on scales we’re used to, they tend to be intuitive. The laws of the very big, small, old, hot, cold, fast, … are the same laws, we just experience a special case (credit goes to the physicist for this paragraph).

There's no reason why everything turns out to be the way it is. That's why science doesn't answer 'why anything happens'. It just tells you 'what works'. And the curvature of spacetime due to the presence of mass works pretty well.

Any theory is a model of the universe. The flat earth being supported by four elephants which are being supported on the back of a turtle which is swimming through space is a theory too, though not a good one. General relativity is also a theory. Einstein postulated that gravity was a pseudo-force which is introduced because the geometry of spacetime is more complicated than the regular Euclidean geometry. Spacetime is curved. This is the general idea of Einstein's theory of gravitation and it 'works' experimentally [better than Newton's gravitation].

But there is no reason why it works; it just does.

This has gotten a little bit too philosophical. As for your second question, read the wikipedia page on Graviton.

I hope this helps! Mursalin Habib · 3 years, 11 months ago

Log in to reply

@Mursalin Habib You just need experience moving near light speed. You can do this in a game simulation. If you want to see visually a world near light speed, check out this game from MIT. David Mattingly Staff · 3 years, 11 months ago

Log in to reply

@David Mattingly the specs,are way beyond my computers capability,sad! Beakal Tiliksew · 3 years, 11 months ago

Log in to reply

@Beakal Tiliksew I don't think it's the specs, more like the game just has a really slow frame rate. My computer is relatively fast, and it still stinks in that respect. Bob Krueger · 3 years, 11 months ago

Log in to reply

@David Mattingly This is ... awesome! Downloading now! Mursalin Habib · 3 years, 11 months ago

Log in to reply

@Mursalin Habib But Here it comes... The universe works quite awesome... But now comes an unproved, but satisfactory answer.

Treat the whole 'universe' as finite, like an ocean. And planets, comets and even neutrons are placed inside it. What will you see? You must put all scientific principles into it. When you see an object moving, you will see that particles will curve around the object. This is viscosity. It is similar to diffraction. If you were to rotate a ball immersed in honey, you will see the honey rotating. Even viscosity is similar to gravitation, in a better way. We see objects when light reflects from it. This is similar to a sound wave reflecting from another surface. Light is similar to sound waves. Even gravitational waves, and they have a constant speed. Redshift, doppler shift, and time dilation is similar to what we experience in our daily life... of sound waves...

This is an idea proposed by me... Don't make quantum mechanics interfere... This an be a big idea... Fahad Shihab · 3 years, 6 months ago

Log in to reply

@Mursalin Habib that means... science is only near truth, also relativity plays on truth also... that it is impossible to theorize the whole world... All are god's creations... Fahad Shihab · 3 years, 11 months ago

Log in to reply

@Mursalin Habib btw, there's now a phrase based on this myth about the turtle that some cosmologists and relativists use when they come across a theory that seems unnatural or contrived: The theory is "turtles all the way down". Stems from here David Mattingly Staff · 3 years, 11 months ago

Log in to reply

@David Mattingly I thought the turtle referred to the "discworld" novels :p Ton De Moree · 3 years, 11 months ago

Log in to reply

A friend of mine recently clarified this in my mind. I think the idea is, any object, even the sun (absent other forces), would accelerate toward the earth at \(9.8 m/s^{2}\). The difference with heavier and heavier objects is that it increases the acceleration of the earth toward the object.

I hope I got this right. Dan Krol · 3 years, 11 months ago

Log in to reply

To understand that,you must derive g first,We know that the force on the surface of the earth is equal to F=mg,we also know F=\(\frac{GM_{e}m}{R_{e}^{2}}\),you see that m cancels out,g=\(\frac{GM_{e}}{R_{e}^{2}}\),it depends on the mass of the earth. Beakal Tiliksew · 3 years, 11 months ago

Log in to reply

Do keep in mind, however, that as the object gets further away from the earth, the acceleration due to gravity decreases. Thus, spacetime does somewhat explain what's going on. Bob Krueger · 3 years, 11 months ago

Log in to reply

By the gravitation equation, all gravitational forces between masses are proportional to the mass. Therefore, since forces are proportional to both mass and acceleration, acceleration is constant. Rogers Epstein · 3 years, 11 months ago

Log in to reply

The same masses that are pulled by the Earth (or any other planet, for that matter) also exert a pull on the Earth by Newton's Third Law. However, masses of everyday objects are very small compared to the mass of the Earth, which means that the difference in gravitational acceleration experienced by two objects of different masses is negligible. I hope this makes sense :) Francis Gerard Magtibay · 3 years, 11 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...