The atmospheric pressure and gravity are very closely related. The force of gravity is acting on mass of gas particles in the atmosphere and pressing towards Earth’s centre. Gravity is a binding, pull force. It is this force that is responsible for increasing pressure, temperature, density and then fusing hydrogen atoms in the belly of stars. read more
there is indeed a relationship between gravity and atmospheric pressure. Gravity attracts matter with mass, in this case gas. The atmosphere being a layer of gas, the stronger the gravity, the higher it's pressure.I If you seal gas in a tank, and increase it's mass (by adding more gas) the pressure will increase. read more