Similar to a galaxy, this force will stretch space from both a hurricanes periphery as well as from its centre. It is of course only a weak contribution, but still important to understand.

Gravity, (acceleration due to gravity "ADG") is the basic to the  the cause of cloud-systems (e.g; west from Africa)  begins to rotate,  - fast  rising vapour and warm air reinforce that process. Later in the process, the coriolis force takes part.

If a hurricane within a radius of 50 km from the center, can carry 1000 liter water per squaremeter the total amount of water in that inner area, the total = 8*10¹² Kg.

This will give an acceleration at the 50 km periphery = 0,0000013 m/s²
After 24 hours, - 86400 seconds an air or water molecule would hence travel would travel with a speed of 0,018 m/s only because of gravity.
This is an average of 0,009 m/s since it started, and a total rotation distance of = 781 meter after 24 hours.

This is based on if the ADG is stable towards the center. If the ADG is increasing it would be faster.

Fast rising warm air will reinforce and speed up the rotating process.

The water amount is based on an assumption, it could be more or less, but is not important. Warm rising air is reinforcing the beginning rotating process, this is important.

The cause of hurricanes only sometimes emerges, - depends first at all on how much mass contributes to encircle a central common point of space (at Africa’s west coast).

This will cause slow acceleration towards the common gravity center. This slow rotation due to gravity can cause a common low pressure, - a process that fast get reinforces by rising warm air.

Even mass (heavy clouds) thousands kilometers away from the gravity center can contribute to establish a common low pressures center, and hence to that a rotation will begin.

Central encircled space will also cause mass attraction between different small low pressure / thunderclouds, and the common center.

This as well can contribute to the rotation of the system, - for example when a small low pressure, is moving faster, (due to eastern the jet wind) than the bigger common low pressure.

These low pressure behaves differently at equator (than for example further north) because of the very fast eastern jet stream most of the time prevents these to rotate; instead heavy thunder clusters of clouds are fast carries away by the strong eastern yet wind stream.

This seems to be the secret of how the dangerous rotation begins.
Sometimes Mr. Gravity makes the rules, - not always, - most of the time Mr Eastern Jet stream is too fast and he makes the rules.

So it is the very beginning of hurricanes and all kind of low pressure we haven’t understood.

The time a low pressure exist  is hence also very  important regarding to how fast wind it will reach. 

Also mass attraction between local and the larger common gravitionelle centre are understood. These are also important factors why a huge low pressure begins to rotate.  The images below speaks for it self. 

Because we have underestimated the strength and importance  of central gravity, we have also failed to understand a very important factor responsible for low pressure (and hurricanes). 

The nature of space and matter has the ability to define a central point, even for the smallest imbalance in space-matter density. Gravity, therefore, automatically outplays itself in circular, self-perpetuating manner.