# Is there a difference between Weight and Force of Gravity?

Is there a difference between Weight and Force of Gravity or they just mean the same thing? My textbook does not clarifies this point.

• According to wikipedia,''In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity.'' – Paul Mar 4 '15 at 12:53

Understanding this question already has an accepted answer, I was confused by this as well and did some additional research that I will share.

The first is the definition of weight. I first understood the definition of weight from the textbook I was reading as the gravitational force that exerts on a body. From this definition, there is no difference between $${F_g}$$, the gravitational force, and $$\vec w$$, weight force.

That said, after re-reading and searching all the internet sufficiently, the definition more accurately used for weight is the gravitational force that the earth exerts on the body or "If you are on another planet, your weight is the gravitational force that planet exerts on you." Young, H. and Freedman, R. (2016). University Physics with Modern Physics (14th ed). Pearson Education, Inc, pp. 114.

With that in mind, typically weight force is a particular type of the gravitational force that refers to the gravitational force on a body (e.g. on the moon, on Mars, on Earth). If you are referring within space such as the gravitational force of Earth on the International Space Station (ISS) or an astronaut on the ISS, they are in constant free-fall, and for sake of clarity, the force causing that free-fall is just called gravitational force since there is the sensation of weightlessness. It would be a misnomer to say how much does an astronaut weigh on the ISS and more accurate to say what is the gravitational force the earth (or the ISS) exerts on the astronaut.

The same can be said of celestial bodies, such as the moon. One would not say, how much does the moon weigh. One would say, what is the gravitational force the earth has on the moon (and so forth for the Earth to the Sun and Mars to the Sun).

When being asked for the weight force, it is generally implicitly understood, it's the gravitational force of an object on the earth (or it will be specifically called out on what body and the acceleration due to gravity on that body, e.g. find the weight force of a person of 68 kg mass on the moon which has an acceleration due to gravity of $$1.620 \dfrac {m}{s^2}$$). When asked for the gravitational force, the 2 object's mass will be provided or the needed data to calculate their mass.

Here is a comparison at the formula/math definitions.

Weight Force: $$\vec w = m\vec g$$ where m is the mass of the object and $$\vec g$$ is the acceleration vector due to gravity (e.g. has both magnitude and direction).

Gravitational Force between 2 objects:

$${F_g} = G * \frac {m_1 m_2}{r^2}$$ where G is the gravitational constant $$\frac {6.67384(80) * 10^{-11} m^3}{kg * s^2}$$ and $$m_1$$ is the mass of object 1 and $$m_2$$ is the mass object 2 with $$r$$ being the distance between the 2 objects.

If we were to calculate both values for 150 lb person at sea level, we would find that both equal $$667 N$$ (rounding to 3 significant figures). To simplify the calculation of gravitational force on the Earth, Newton derived the weight force relationship.

Hope this helps.

While both are forces, weight is generally specific to any sum of forces you feel reciprocated as a normal force (or tension). I can feel heavy in a centrifuge because of the centrifugal force. When I find myself sitting in my chair (safely away from centrifuges) the astronauts on the International Space Station and I are both are subject to the force of gravity--but only I will feel my weight in my chair as the chair pushes back up against me. The astronauts are in free fall and do not feel the sensation of weight ignoring tidal effects.

Weight is a subtle concept, because we are so used to it we don't even notice it anymore. You'll find surprising how badly some students grasp the concept of weight, despite the fact they are firmly sitting on a chair in the very same moment.

Anyway, weight is the force an object experiences when inside a gravitational field. That means me, you, StackExchange servers, air, but even ISS, which is orbiting apparently "weightless", experience weight. You can be tricked to feel less or more heavy by applying other forces, for example in a centrifuge, on a roller-coaster, or when accelerating inside a car.

Even when you are free-falling you are experiencing weight, in fact it's exactly the reason you're falling down.

But weight is not really gravity, because sometimes it doesn't really make sense to speak about weight, even in a gravitational field.

First, whereas you can have gravity without weight (e.g. light is bended by gravitational fields, altough it has not weight, because it is massless), you cannot have weight without gravity.

Second, gravity acts both ways: as Earth is pulling you down on the ground, you are pulling Earth "up" with the same strength. Thus by talking only about your weight you're being a little selfish and hurting Earth's feelings, as well as Newton's third law's.

• I don't agree with your penultimate paragraph. The first sentence should surely read, "...you can have gravity without $mass$..." This is surely equivalent to "You can have weight without mass" and does not in any way imply that you can have gravity without weight. – Philip Wood Mar 12 '19 at 13:19
• Yeah you're probably right, but I was trying to avoid speaking about mass etc. since my goal was to keep it simple and relatable. Or at least I think that's what I was trying to achieve four years ago. On the other hand, I feel "weight" in more general situations doesn't really apply anymore. It's weird to speak of "Earth weight wrt the Sun" or "light weight". I guess I was trying to convey this in that sentence. – mattecapu Mar 13 '19 at 11:09

Weight is the force experienced by a body due to the gravity of the earth, a planet, a particle, or another body. The Force of gravity is the force that brings about weight.

Physics texts are regrettably nonuniform in their usage of the term "weight." Here's a useful definition of weight. Your weight is numerically equal to the magnitude of the force that gravity exerts on you. But weight and gravity are not synonyms, as is seeming to be implied. Have you ever heard the expression about being weightless in outer space or when you're free falling? That doesn't mean there's no gravity in outer space or that it isn't gravity causing you to fall. Gravity as a vector force points downwards. Your weight is the UPWARDS force that the floor (or a chair) is exerting on you that counteracts gravity and keeps you from falling towards the center of the earth. (Rereading things, I believe I said what Andrew said, just differently.)

Weight is a pre-science concept which has been retrofitted into the framework of Newtonian mechanics. Not surprisingly, this retrofitting is not always consistent and is sometimes at odds with natural language usage and our intuition. For example, consider the following questions:

• Does a spring balance/strain gauge measure weight ? Is it always correct ? Does a beam balance measure weight ?

• Does your weight change depending on your location on the Earth e.g. at the poles, at the equator, at the top of Mt Everest, at the bottom of the oceans ?

• If it were possible to drill a hole hundreds of km deep, how would your weight change at different depths in the hole ?

• What does a parachutist weigh (a) when they step out of the plane, (b) when they reach terminal velocity and (c) when their parachute opens ?

• What does a balloon filled with air weigh ? Does its weight change depending on altitude ? What does a balloon filled with helium weigh ?

• What do the astronauts in the ISS weigh ?

• What would you weigh at the L1 point between the Earth and the Moon ? What would you weigh at the L1 point between the Earth and the Sun ?

The difference is that weight is a consequence of the Force of gravity. Weight is a quantity that you measure for a particular object, while gravity is a measure of how curved is the spacetime where that object is living. To understand better this difference, think about a light beam traveling along the space. You can't measure the "weight" of the light beam, however, the light beam will not travel in a straight line if the effects of gravity are considerable.