# Is the weight of an object moving at escape velocity equal zero?

If an object would be accelerated to the escape velocity would it's weight be equal to zero?

Say I throw a ball from Earths surface (assuming frictionless atmosphere) upwards at 11.186km/s is it's weight equal zero? I assume mass would be greater because energy is greater but what about weight?

• The ball is weightless when it is freely falling regardless of whether it has escape velocity or not. As soon as the ball leaves your hand, it is in free fall and so has zero weight. Nov 27, 2017 at 0:55
• Is it's weight unchanged then? Nov 27, 2017 at 0:55
• Are all gas molecules weightles as they swing around? Nov 27, 2017 at 0:58

Say I throw a ball from Earths surface (assuming frictionless atmosphere) upwards at 11.186km/s is it's weight equal zero?

The ball is weightless when it is freely falling regardless of whether it has escape velocity or not. In your example, as soon as the ball leaves your hand, it is in free fall and so has zero weight.

From the Wikipedia article Weight:

Thus, in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless. Ignoring air resistance, the famous apple falling from the tree, on its way to meet the ground near Isaac Newton, is weightless.

The weight is not zero in free fall, it is just not in equillibrum (ignoring air-friction) with another force.

The weight may vary with the gravitational potential and not with the acceleration of the object (given for other forces then the gravitational), nor with its velocity.

• Is that a yes to my question? :) Nov 27, 2017 at 11:29
• It sounds (correctly) like a NO to me. Nov 27, 2017 at 13:14
• Quick question for the Rodrigo: after the ball is released, what is the acceleration of the ball as read by an accelerometer attached to it? Nov 27, 2017 at 13:37
• The thing is: are you thinking in the newtonian picture, or in einstein picture? The accelerometer reads g. From a point of view of Newton, it is not an inertial observer, so their readings are not trustable to comply with newtonians law... From an Einstein point of view there is no such thing as weight... The weigth doesnt vary with velocity... (Already stated above), so no. Nov 27, 2017 at 14:38
• Rodrigo, I suspect that you misread my comment because the accelerometer attached the ball reads zero after the ball is released. Nov 27, 2017 at 16:31

According to the Newtonian model of mechanics, massive bodies exert forces on other massive bodies, even if one of the bodies is in free fall. We refer to this as the weight of the body. So, bodies, even in free fall, have weight.

According to the General Relativity model of mechanics, massive bodies do not exert forces on other massive bodies (unless the bodies are in contact). There is no such thing as gravitational force, so bodies do not have weight.

• "So, bodies, even in free fall, have weight." - not according to the operational definition of weight. See, e.g., THE IMPACT OF AN OPERATIONAL DEFINITION OF THE WEIGHT CONCEPT ON STUDENTS’ UNDERSTANDING Nov 27, 2017 at 15:44
• A quote: "Weight is distinguished from mass and is often defined as the force of gravitation exerted on a particular object (“gravitational weight” approach). The complexity of this pedagogy can be appreciated if one pays attention to the conceptual break: the heaviness of objects is directly associated with weighing results and so corresponds to the operational definition. Instead, when weight is equated with the gravitational force, weighing results become unreliable since the interpretation of weighing is not univocal." Nov 27, 2017 at 15:48
• This is all correct within the framework of Newtonian mechanics. Within the framework of Relativistic mechanics, none of it is correct. So it all depends on which model one is using, and on its applicability/limitations to your particular situation. Most people are comfortable working, where appropriate, with either approach. Under typical practical conditions, the error incurred by applying Newtonian mechanics is acceptable. But don't try to use it to predict the precession of the elliptical orbit of Mercury. Nov 27, 2017 at 16:29