Weight in Orbit? 0N on Spring Balance at 2.8M Triton Ht

[pivoxa15]

Homework Statement

It was established that the gravitational field strength at a height of 2.8*10^6m above the surface of Triton is 0.79N/kg.

If a spacecraft was orbiting Triton at a height of 2.8*10^6m above the surface with a constant speed, what would be the reading on a spring balance in the spacecraft if a mass of 10kg was placed on the end of it?

The Attempt at a Solution

I think it is 0N because a spring balance cannot weigh mass when in orbit. This is because everything in orbit is perpetually in freefall and moving at a constant speed. Everything on that spaceship is weightless. There is always a gravitational field felt by every object in the spacecraft but the objects are perpetually falling in this field but without changing its distance from Triton because it is moving in a circle so the magnitude of this field is constant as well. There is no acceleration in any reference frame for every object in the spacecraft . In other words, no object experiences a reaction force even though every object experiences a force towards Triton. So no tension exists in the spring balance because every object accelerates in the same direction and with the same magnitude. This is the reason why no weight can be measured. Is my analysis correct? The answers just evaluated assuming the spring balance worked and got 7.9N.

 

[D H]

Your analysis is correct. A scale (like any other accelerometer) measures the acceleration of a body due to the total force acting on some body except the gravitational force.

From the perspective of General Relativity, this is even easier to state: A scale (like any other accelerometer) measures the acceleration of a body due to the total force acting on some body, period. (Gravity is not a force in GR.)

 

[eaboujaoudeh]

i have a question about this subject. r u assuming that the rotational gravitational pull is cancelling the gravitaional pull by Triton?

 

[D H]

I am assuming no such thing, as there is no such thing as "rotational gravitational pull".

 

[eaboujaoudeh]

sorry not rotational,. potential ! sorry misconcentration

 

[eaboujaoudeh]

my god ! wrong window again.. well what is cancelling the gravitational pull form the planet to the person in space? i meant rotational sorry..

 

[D H]

There is nothing to be canceled. No device can be made that directly measures the gravitational "force", including a scale. Your bathroom scale does not measure gravitational force. It measures the upward force exerted by the ground on the bottom of the scale that prevents the scale from falling through the floor toward the center of the Earth.

 

[eaboujaoudeh]

the upward motion is a reaction to ur weight ur exerting on the scale, which is gravity induced. in space gravity is less but u still have weight, thus u still might put tension on the spring !

 

[D H]

There are two kinds of weight: weight tautologically defined as the force due to gravity, and the weight that a scale measures. Your scale measures everything but gravity.

Suppose you are standing on a scale in an elevator car at the top of a tall building. Your scale registers your normal weight when the elevator car is stationary. Suppose now that the cable snaps and the car with you and the scale inside go into free-fall. You will feel "light as a feather", and your stomach won't like it a bit. While your tautologically-defined weight hasn't changed a bit, the scale will register zero.

 

[eaboujaoudeh]

that's because u have another acceleration that cancels the gravity factor,here the acceleration is equal to gravity of free fall this is why u feel weightless. try this what if the elevator was accelerating with a value A less than that of gravity, u'll feel difference in weight! but in space what is the substitute to acceleration in the first example

 

[D H]

What cancellation? The free-falling elevator car is accelerating precisely because it is subject to gravity and nothing else. The scale registers zero precisely because it is subject to gravity and nothing else. A space vehicle orbiting some planet is constantly falling. It is subject to gravity and nothing else, which is why the crewmembers in the vehicle feel "weightless".

 

[eaboujaoudeh]

OMG now i see. it means that you and the scale are moving at the same gravitational pull thus no weight will be displayed.

 

[pivoxa15]

There is nothing to be canceled. No device can be made that directly measures the gravitational "force", including a scale. Your bathroom scale does not measure gravitational force. It measures the upward force exerted by the ground on the bottom of the scale that prevents the scale from falling through the floor toward the center of the Earth.

In space there is no upwards force exerted by the ground on the bottom of the scale. Would you call this upwards force the normal force exerted from the ground/scale to you. So it's an action/reaction pair. You exert a force to the scale which passes down to the ground and the ground which is stationary in return exerts an upwards force to the scale which passes to your feet. In this way, your weight can be determined.