Gravitational Force in “Gravity”

“Set me free, leave me be
I don’t want to fall another moment into your gravity”
– Sara Bareilles, “Gravity”

Sorry, Sara Bareilles, but you can’t avoid someone’s gravity.

OK, I realize Sara Bareilles is singing about a m*etaphorical force between people that she wants to avoid, but there really is a physical gravitational force between people.

Gravity is a force of attra*ction between all things with mass or energy. Gravity is all around us. For example, the Sun keeps the Earth (and other planets) in orbit. Earth’s gravity keeps the moon in orbit. The gravitational force from the Sun and the Moon cause the tides of the ocean. The Earth causes dropped objects to fall to the ground. The Earth also holds us to the ground and keeps together our atmosphere.



Gravitational force between two objects depends on two things. One, gravitational force depends on the masses of the two objects. The more mass an object has, the stronger the gravitational force it will exert. Conversely, the less mass an object has, the weaker the gravitational force it will exert. Two, gravitational force depends on the distance between the two objects. As the two objects move closer together, the gravitational force gets stronger. As the two objects move farther apart, the gravitational force gets weaker.

This relationship can be described through Newton’s law of universal gravitation:

F = G x (m1m2)/r2

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses. The value of G is 6.67 x 10-11 Nm2kg-2. (N stands for Newton, a measure for force. One Newton is equal to one kilogram-meter per second squared, or the force required to accelerate an object with one kilogram of mass one meter per squared second.)

The above equation can be used to calculate the gravitational force between two objects, such as the Earth and the Moon. The Earth has a mass of 5.97 x 1024 kilograms, the Moon has a mass of 7.35 x 1022 kilograms, and the average distance between the two is 3.78 x 108 meters. By plugging these numbers into Newton’s law of universal gravitation, we get 2.05 x 1020 Newtons as the gravitational force between the Earth and the Moon.

Gravity doesn’t just involve planets, moons, stars, and other cosmic objects- technically, there’s gravity between smaller objects as well. For example, take people. The CDC gives an average weight for men in the United States at 197.8 (89.72 kilograms) pounds and an average weight for women in the United States at 170.5 pounds (77.34 kilograms). Let’s just average those two numbers to 184.15 pounds (83.53 kilograms). And let’s say the two people are 1 meter apart. Plug the numbers into Newton’s law of universal gravitation and you get 4.65 x 10-7 Newtons (0.000000465 Newtons)- much, much lower than the value for the gravitational force between the Earth and the Moon.

So while there is a gravitational force between you and another person, you don’t notice it at all, due to its miniscule effect and larger forces (gravitational and others) at play around us. We’re really not that massive to cause any real effect on most other objects.

After all, we are just specs on a slightly larger spec in this vast universe.



Keep calm and science on.