[pharmacist2030 (OP)]

I was asked by a friend which has a higher gravitational force a red giant or a neutron star? I know that a neutron star is the product of the explosion of a red giant   ( supernova) I read in a book before that a neutron star has a higher gravitational force but it doesn't make sense to me as a red giant is bigger in size and the energy wasted in the explosion, how does it create a neutron star with a higher gravitational force? I hope that someone can clarify this to me. Thanks

[MurBob]

I was asked by a friend which has a higher gravitational force a red giant or a neutron star? I know that a neutron star is the product of the explosion of a red giant   ( supernova) I read in a book before that a neutron star has a higher gravitational force but it doesn't make sense to me as a red giant is bigger in size and the energy wasted in the explosion, how does it create a neutron star with a higher gravitational force? I hope that someone can clarify this to me. Thanks

While I neutron star is the product of a supernova, I believe a white dwarf is actually the product of a burned out red giant.   
Physical size and mass are two different measurements.   Size is a distance measurement where mass is a measurement of how much matter.
Take a pound of lead and a pound of feathers.  Which is larger?  The feathers are, but the two items weigh the same amount, they have the same mass.

As I understand it, a neutron star is formed when a massive star of around 10 times the MASS of our sun goes supernova.  The matter inside the star collapses.. now, normally the center region of all stars collapse when the star runs out of energy..  but what makes a larger star different is something called degenerate pressure.   When a normal star like our sun blows off its outer layers as a reg giant, the core collapses and gets denser and denser until electron degenerate pressure stops any further collapse. This is called a white dwarf.     If the star is a big one, like around 10 times the mass of our sun, the collapsing core can have enough mass to overcome the electron degenerate pressure.   This extra pressure causes the electrons and protons to combine and form neutrons and the core continues collapsing until neutron degenerate pressure stops is from going any further.   Really really massive stars that are around (25?) times the mass of the sun have enough mass that the core is capable of overcoming even the neutron degenerate pressure.. once that happens, they collapse into a black hole.   

[chiralSPO]

The missing piece here is the radius of the star. A red giant is more massive, but it is much, much less dense than a neutron star, so if one is discussing the gravitational force at the surface of the star, then the neutron star will by a large margin (a = GM_star/r², so if M_{neutron star} is 0.01 M_{red giant}, but R_{neutron star} is 0.00001 R_{red giant}, then surface a_{neutron star} = 10000000 a_{red giant})

If one is concerned with the gravitational force far from the star, then the more massive red giant wins, but if the distance in question is less than the radius of the red giant, then the neutron star will almost certainly win.

[MurBob]

The missing piece here is the radius of the star. A red giant is more massive,

A neutron star has about 1.1 to 2 solar masses (IE: its 1.1 to 2 times heavier (massive) than our sun).  When our sun turns red giant, a neutron star will still have more mass. 

If a star that was more than twice the mass of our sun (>2 solar masses), then it would be more massive as a red giant than a neutron star.

[MurBob]

And just for fun...
If you scaled down the size of our sun to the size of a standard basketball (9 inches), earth would be a bit larger than a grain of sand (.08 inches) and be about 80 feet away.   Earth has a diameter of almost 8000 miles while a neutron star is only about 7 miles in diameter.

[pharmacist2030 (OP)]

 Earth has a diameter of almost 8000 miles while a neutron star is only about 7 miles in diameter

By this example you mean that the size of the Neutron star will be the size of an atom compared to the size of Earth the grain of sand )) but if the Neutron star is denser than the Earth that means it will have a stronger gravitational force than the Earth? 

[pharmacist2030 (OP)]

To put the question in other words, imagine a red giant in front of a neutron star which one will attract the other?  which one has the more power and force to attract the other?

[chris]

A neutron star has about the same cross-sectional area as a small town yet crams one and a half times the mass of our own Sun into that relatively tiny volume. Mind-boggling isn't it?

[MurBob]

Earth has a diameter of almost 8000 miles while a neutron star is only about 7 miles in diameter

By this example you mean that the size of the Neutron star will be the size of an atom compared to the size of Earth the grain of sand )) but if the Neutron star is denser than the Earth that means it will have a stronger gravitational force than the Earth?

Without actually doing the math, I would say not the size of an atom but more like a red blood cell...   

[MurBob]

A neutron star has about the same cross-sectional area as a small town yet crams one and a half times the mass of our own Sun into that relatively tiny volume. Mind-boggling isn't it?

Lets get some more scale involved so we get a feel for things.   This time, lets blow up an atom so that the proton(s) in the center are the size of a tennis ball.   At this scale, the electron(s) in orbit would be about 3 miles away from the proton in the center and be about the size of a grain of sand.   

Everything in between the collection of tennis balls (protons) in the center, and the orbiting electron 3 miles away, is empty space!!    That's right, all normal matter like  you and I and my desk and car, is basically 99.9999999(add more nine's) empty space!!    That's amazing to me.

Electron degeneracy pressure supports that empty space (white dwarf and all other normal matter like you and I and my desk)..   So, in essence, when enough pressure is applied, the electron degeneracy pressure is overcome and the electron is squeezed into the protons to transform them into neutrons..  when that electron collapses, all that empty space can now be occupied!   

That's why neutron stars are able to become so small and so dense.

When you crack open a neutron, you find the same type of arraignment inside except this time we call them quarks.   The same basic process happens to collapse the neutron degeneracy pressure into a black hole..   (or as some theorize, a quark star)

[evan_au]

which has a higher gravitational force a red giant or a neutron star?

An aspect which is left undefined in the question is whether we are talking about different stars, or the same star at different points in its lifecycle?

If we are talking about different stars:
- Betelgeuse has a far higher mass (and thus far higher gravity at large distances) than any neutron star.
- Small red giants have a lower mass  (and thus lower gravity at large distances) than the smallest neutron star
- So the answer can be "both"

If we are talking about the same star:
- Medium-sized red giants will form a neutron star, but will lose a large amount of mass during the red giant phase. Even more mass is lost during the subsequent supernova explosion. So the resulting neutron star will have far lower mass (and thus lower gravity at large distances) than when it started as a red giant.
- Smaller red giants will turn into white dwarf stars, and will not form a neutron star
- Red Supergiants like Betelgeuse are expected to form a black hole rather than a neutron star
- So the answer is "the red giant" (for some red giants)

Note: This clarification does not change the answer above that the surface gravity of a neutron star is always greater than the surface gravity of a red giant.

Background
- Red giants have masses around 0.3-8 solar masses
- The related class of red supergiants (like Betelgeuse) are around 10 to 40 solar masses.
- Neutron stars have masses around 1.1-3 solar masses, which is smaller than the range of red giants

During the Red giant phase, a given star will lose a large fraction of its mass; Red Supergiants seem to drop down to about 10 solar masses. This occurs because the outer atmosphere is weakly attached to the star, and strong stellar winds blow away much of the star's atmosphere, forming a planetary nebula.

[Space Flow]

The simple answer is that Gravity is defined by the amount of mass within a given radius.

It doesn't matter what form that mass takes within the specified radius. Gravity doesn't care how compact or diffuse that mass arranges itself in or even how many separate bodies go to making up the total mass inside the specified radius. Just the total amount of mass enclosed.

So as presented your question has no way to an answer as the right data is not provided.

You need a figure for Mass and a figure for radius or you can not ask the question; "How much gravity"

That should also answer the second part of your question as to how a Neutron star can have a higher gravity than a more massive Red Giant.
It is all about Mass inside a radius.
By packing more Mass inside a smaller radius you end up with a higher surface gravity.
Just remember Mass and Radius.