# Suppose you have an object with infinite mass

#### arandomtheoris

Now you put the object right above the Earth's surface, like just a few meters above the ground.
Let's just assume the object will have no gravitational affect against the Earth, or any object for that matter. It's defying logic, I know, but let's just roll with that.
Assuming the object would require infinite energy to move, would the Earth's gravity be able to pull it down to the ground (option #1) , or would it float in the air, unable to move at all? (option #2)

Answering option #1 would imply gravity is a force with infinite power
Answering option #2 would imply that the law that states all objects move at the same speed towards an object with a gravitational pull is in fact incorrect.

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#### russ_watters

Mentor
Welcome to PF!

Unfortunately, your assumptions are both unphysical and self-contradictory. You say in different areas, that gravity doesn't apply and that it does. So which is it?

A possible answer though is that gravitational force between objects pulls both objects toward the other. And the one that moves more (from a 3rd party, inertial frame) is the less massive one.

#### Bobbywhy

Gold Member
An object of infinite mass does not and cannot exist. So, why bother making some thought experiment using an impossible object?

#### Nugatory

Mentor
Obviously you can't really have an object of infinite mass, but you can do the next best thing and assume that the mass of the object is enormously large compared with the mass of the earth... Maybe, for example, 5x1024 times the mass of the earth?

Place an object of that mass a few meters away from the surface of the earth, and we have the exact same problem as if we we had a one kg mass a few meters from the earth: a light object and a heavier (by a factor of 5x1024) object separated by a few meters. What happens?

You may be confusing yourself by trying to simplify things with the assumption that your object has "no gravitational effect against the earth, or any object for that matter". As you point out, that assumption may defy logic - but an even bigger problem is that it defies Newton's third law. If the earth is to exert a force on the object, then the object must exert an equal and opposite force on the earth; if you don't allow for this, you won't be able to get any sensible results out of your thought experiment.

#### ZapperZ

Staff Emeritus
2018 Award
Now you put the object right above the Earth's surface, like just a few meters above the ground.
Let's just assume the object will have no gravitational affect against the Earth, or any object for that matter. It's defying logic, I know, but let's just roll with that.
Assuming the object would require infinite energy to move, would the Earth's gravity be able to pull it down to the ground (option #1) , or would it float in the air, unable to move at all? (option #2)

Answering option #1 would imply gravity is a force with infinite power
Answering option #2 would imply that the law that states all objects move at the same speed towards an object with a gravitational pull is in fact incorrect.
You apply one set of rules on one, and you apply a different set of rules to the other. This not only defies logic, it is also nonsensical.

The thing about "thought experiment" is that it has to be consistent. Otherwise, you are making up the rules as you go along. Garbage in, garbage out.

Zz.

#### HallsofIvy

Homework Helper
If you had an object of extremely great mass (not infinite mass- there is no such thing) a few meters above the surface of the earth, yes, the earth would attract the obect- at the same 9.8 meters per second per second it attracts anything. But the object would be attracting the earth at a much greater acceleration. Whether you would see the object "falling" toward the earth or the earth "falling" toward the object would depend upon your frame of reference.

#### BiGyElLoWhAt

Gold Member
F=$\frac{M_{1}M_{2}}{r^{2}}$G

Also:

$F_{1 on 2} = -F_{2 on 1}$ (Newtons 3rd law), If our immense object cannot exert a gravitational force on earth, then earth cannot exert a gravitational force on our immense object.

#### etudiant

Gold Member
As HallsofIvy has so succinctly pointed out, the earth as the less massive object would accelerate much more towards the object than the object would accelerate towards the earth.
So you can envision the earth sloshing around the object, reforming with the object at its center. Would make for an hellacious special effects video, but no fun for the current surface dwellers.

#### DrStupid

Suppose you have an object with infinite mass
[...]
Let's just assume the object will have no gravitational affect against the Earth, or any object for that matter.
An infinite homogeneous mass distribution with a spherical hole containing the Earth would do the job.

Assuming the object would require infinite energy to move, would the Earth's gravity be able to pull it down to the ground (option #1)
Of course not.

or would it float in the air, unable to move at all? (option #2)
It will remain in its state of motion.

Answering option #2 would imply that the law that states all objects move at the same speed towards an object with a gravitational pull is in fact incorrect.
There is no gravitational pull.