# Effect of water displacement on gravitation pull between ships

• jims
In summary, the gravitational attraction between two large, full oil tankers whose sides are touching would be 1,331 lb., given the mass of each ship as 6.5 x 10^8 kg, distance between their CG's of 69 m, G = 6.674 x 10^-11 N(m/kg)^2, and 1 N = 0.2248 lb.
jims
I calculated, using Newton's formula F = GmM/r^2, that the gravitational attraction between two large, full oil tankers whose sides are touching would be 1,331 lb., given the mass of each ship as 6.5 x 10^8 kg, distance between their CG's of 69 m, G = 6.674 x 10^-11 N(m/kg)^2, and 1 N = 0.2248 lb.

The question is this: Does the water displaced by the two ships add, subtract, or have no effect on the force I feel if I am trying to hold the ships apart? and why?

Compared to what? It's a little like asking if the number 5 is happy.

If the water were instead inside the ships and they were just barely afloat, you can recalculate a larger attraction. If you calculate the attraction with the ships out of the water on an ideal frictionless surface you'll get your same answer. If they are on a typical real world surface with friction you'd measure no attraction but maybe calculate the same theoretical figure as you did because they'd be stuck in place on a dock or other surface.

It would be better to think of your question with the ships empty or less full...or refilled with a liquid of different density...then you can easily answer your own question.

Naty1 said:
Compared to what? It's a little like asking if the number 5 is happy.
...
If you calculate the attraction with the ships out of the water on an ideal frictionless surface you'll get your same answer...

Sorry if my question seemed trivial. At first I thought that the "holes in the water" formerly occupied by the displaced water might be modeled as having a gravitational repulsion to each other, due to all the surrounding water's gravitational attraction to itself. But each hole actually has a ship of the same mass sitting in it. So there is no lateral pull on the water and no lateral pull of the water on the ships. Thanks for your help.

jims said:
Sorry if my question seemed trivial. At first I thought that the "holes in the water" formerly occupied by the displaced water might be modeled as having a gravitational repulsion to each other, due to all the surrounding water's gravitational attraction to itself. But each hole actually has a ship of the same mass sitting in it.

Even if the holes were not filled, they would rather attract than repulse each other.

A.T. said:
Even if the holes were not filled, they would rather attract than repulse each other.

Nice thought! I enjoy wondering about holes in the water. Not sure, but I think the holes might repel. Check out this hand-waving:)

Think of a volume of ocean with motionless water.

At a given depth beneath the surface, we make appear two ideal spheres. Since these perfectly massless, rigid, and watertight spheres have ideally thin walls, no water has yet been disturbed.

Since gravity is universal, the water inside one sphere is attracted to the water inside the other sphere with a force given by Newton’s F = GmM/r^2. But the spheres remain motionless because of offsetting forces of gravity from the surrounding environment.

Next we tie each sphere to the ocean bottom, using ideally strong, thin, and massless ropes. Each rope is attached in its line between its sphere’s water’s center of mass (CM) and the earth’s CM.

Then we make the water inside the spheres disappear, creating two holes in the water of mass zero, thereby removing the earlier mentioned force of attraction.

Absent this force of attraction, I think the holes would be pulled apart by the “forces of gravity from the surrounding environment” mentioned earlier. When the system again comes to rest, I think each rope would be pulling against an upward buoyancy vector plus a smaller lateral vector of f = GmM/R^2, where R > r.

## 1. How does water displacement affect the gravitational pull between ships?

Water displacement refers to the amount of water that is moved or displaced by a ship as it floats. This displacement creates an upward force called buoyancy, which counters the downward force of gravity. Therefore, the greater the water displacement of a ship, the greater the buoyancy force and the less the gravitational pull between ships.

## 2. Does the shape of a ship affect the water displacement and thus the gravitational pull?

Yes, the shape of a ship can affect the amount of water it displaces, which in turn can affect the gravitational pull between ships. Generally, a wider and flatter ship will displace more water and have a greater buoyancy force, resulting in a weaker gravitational pull compared to a narrower and taller ship.

## 3. How does the distance between ships impact the gravitational pull?

The gravitational pull between ships is inversely proportional to the square of the distance between them. This means that as the distance between ships increases, the gravitational pull decreases. Therefore, if two ships are closer together, the gravitational pull between them will be stronger compared to when they are farther apart.

## 4. Can the gravitational pull between ships be completely eliminated by manipulating water displacement?

No, the gravitational pull between ships is a natural phenomenon and cannot be completely eliminated. However, it can be weakened by manipulating water displacement through changing the shape, size, or distance between the ships.

## 5. Are there any other factors besides water displacement that can affect the gravitational pull between ships?

Yes, other factors such as the mass and density of the ships, as well as the mass and density of the water they are displacing, can also impact the gravitational pull between ships. Additionally, external forces such as wind, currents, and tides can also affect the water displacement and thus the gravitational pull between ships.

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