Mcc asked in Science & MathematicsPhysics · 1 month ago

# Why is gravitational potential always negative ?

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• 1 month ago

Gravity was negative for an extremely brief period during the inflationary phase of the Big Bang. For more on that, read some of Alan Guth's writings.

• 1 month ago

It is not always negative. It depends on your coordinate system. Basically, if y-axis positive goes up (like in mechanics, rather than calculus) then altitute increases with height..... If I set myself above you and make that my zero point, then your altitube is negative.

Then there is g. You have to decide what sign you will give g. If y-axis goes up, g is negative (cuz duh, g is a force acting DOWN).

then, Ep=g*h*m. so then, its negative when g and h don't have the same sign. Else its positive.

• Amy
Lv 7
1 month ago

Gravitational force is F = GMm/R^2.

When we integrate that with respect to distance, we get U = -GMm/R

In practice it doesn't actually matter whether it's positive or negative because we only ever use the DIFFERENCE in potential between two locations. But we have to pick some place to be our reference point that has zero potential energy.

For problems involving thrown balls, it makes sense to have "the ground" as zero. An object's potential energy is then U = mgh, ignoring all of the potential to be pulled further down than that.

ΔU = (-GMm/(R+h)) - (-GMm/R) = GMmh/(R(R+h)) ≈ GMmh/R^2 = gmh

But when discussing satellite orbits, there's nothing special about the surface of the Earth/Sun/other gravitational source. It would make a lot more sense to use the center of the gravitational source as zero. Unfortunately, the difference in potential energy between there and anywhere else is infinite.

ΔU = (-GMm/R) - (-GMm/0) = ∞

The only other special place is infinite distance. So we make that 0, and since everywhere else has less potential, their values are negative.

• 1 month ago

Isn't always negative.  We can actually set its zero point anywhere and then the negative potential energy region will be derived from that zero point.  EX:  We often set P = 0 = mh when h = 0 height above the ground level.  In which case any h > 0 gives us a positive potential energy.

But we typically choose it to be zero at infinity when a point finally loses all its kinetic energy K; so that total energy T = K + P = 0 at infinity.  And from the conservation of energy, the total energy of the universe must remain at net zero.

But as a point is captured by a gravity force and it accelerates towards the source of that force its kinetic energy, K, begins to rise.  And, ta da, with K becoming more and more positive, P the potential energy must become...more and more negative to keep T = 0 throughout.  In other words, P is often, not always, negative because we often, not always, set its zero point at infinity.

• 1 month ago

Well if you think gravitational cant be negative, then try to imagine this if the gravity is positive on Earth then everything on Earth goes upside down. In other words, you become Ironman without iron-suite.

• 1 month ago

The gravitational potential energy between two masses at infinite separation is naturally zero since they can't know each other's existence. (As the gravitational field generated by one mass is zero at the location of the other mass.) When the two masses move toward each other due to their mutual gravitational attraction, their velocities increase, implying that the kinetic energies of them also increase, hence the potential energy between them must be dropping --- from zero in fact! This is due to the fact that the total energy among them must be conserved. That means the potential energy between them must be negative when they are at any finite separation, and more negative at shorter separation between them! There is no ambiguity in this argument --- not involving an arbitrarily set zero point for the potential energy.

Source(s): I am a retired university physics professor in the US.
• 1 month ago

There is a reason for this convention.  We need some universally acceptable reference point that makes our analyses of the universe as simple as possible.  If we define outer space, a long way from any body, as zero then as you are attracted by a planet you are given work and energy.  Possibly as kinetic.  But that means that the amount of energy left in the gravitational potential is less.  ie it is now a negative.  We use the same convention for electrons around an atom and for nucleons within the nucleus.   Or even for things like sticky tape.  If energy MUST BE ADDED to break something free then the potential prior to this is taken as a negative.  It is merely a convention but we use it consistently everywhere.

• neb
Lv 7
1 month ago

You can define the zero point of gravitational potential - just like every potential - any where you like. The value of the potential at any SINGLE point - and it’s sign - is physically meaningless. What has physical significance is the DIFFERENCE in potential between two points.

So let’s say we arbitrarily declare the gravitational potential as +5 at a particular height above the ground. We drop a rock. Let’s say the rock gains 3 units of positive kinetic energy (always positive) by the time it hits the ground. In order to conserve energy, that means the gravitational potential must have decreased by -3 units, and must now be at a value of +2 on the earths surface. So, we see that as the rock gets closer and closer to earth it’s gravitational potential gets more and more negative.

So, when we say the potential of a gravitational field is negative, we really mean physically that it gets more and more negative as you approach the gravitating source. Generally, it’s a convention to take the arbitrary zero point to be infinitely so the field is negative everywhere, but it is also common to pick the zero point on the earths surface for simplicity.

• Jim
Lv 7
1 month ago

It's not.  Sure, normally we'd see it that way standing on earth and lifting things "up".

But what if we lifted something on the other side of the earth? Then it would be positive.

• 1 month ago

Have in mind that this is about convention.

Usually, in Newtonian gravity,

the gravitational potential at a location is equal to

the work (energy transferred) per unit mass

that would be needed to move an object to that location

from an infinite distance away, without a change in speed.

You might notice that if we start far away from a mass, we will be attracted to it without doing anything. To not gain speed, we actually need to be braking which requires (negative) work.

That work happens to be -GMm/r, for two point masses M and m.

So potential is work per unit mass = -GM/r.

Inversely, if we want to escape from distance r to somewhere very far, we need to do (positive) work GMm/r.

If there is more than one mass significantly affecting the gravity at a location, we just add up all their -GM/r.

So, the answer to "is gravitational potential always negative?" is of course not, since we could specify any other position besides infinity.

For example, at the surface of the Earth, we often define potential to be 0 at ground level.

We don't care about infinity, and the strength of gravity is basically the same at any height.

Potential:

V(h) = g*h, where h is distance above the floor.

Such that the work needed to raise mass m from ground to height h is m * g*h

The "exact" equation would be V(h) = GM(1/r - 1/(r+h)), where r = Earth radius

Compare g*h and GM(1/r - 1/(r+h)) for "small" values of h (under 500 km)