How do you determine the mass of an object moving at a constant velocity?

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Discussion Overview

The discussion revolves around methods to determine the mass of an object moving at a constant velocity without altering its state. Participants explore various theoretical approaches, including gravitational interactions and orbital mechanics, while addressing the challenges associated with such measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests measuring the acceleration of two test masses placed near the object to infer its mass, while another asks for clarification on this method.
  • There is a discussion about Newton's universal law of gravitation and how it relates to the mass terms involved in the formula.
  • Some participants express confusion about how to find acceleration and whether the accelerations of the test masses would be the same when close to the object.
  • Another approach proposed involves matching velocity with the object and measuring the period of an orbit, though this is noted to change the object's velocity.
  • One participant argues that any measurement will inherently involve some interaction with the system, suggesting that a small change in velocity is acceptable in classical mechanics.
  • Another participant mentions using light beams to measure gravitational effects as a potential method for determining mass.
  • There is a reiteration that the mass of the test objects is crucial for calculating the mass of the object in question.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of measuring mass without altering the object's state. While some methods are proposed, there is no consensus on a definitive approach, and several participants highlight the inherent challenges and assumptions involved.

Contextual Notes

The discussion includes assumptions about the sizes of test masses and the nature of gravitational interactions, as well as the implications of measurement techniques on the system's state. The necessity of knowing the mass of test objects to determine the mass of the moving object is also emphasized.

Thejas15101998
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A object is moving in free space with a constant velocity. How will you find the mass of the object without changing its velocity ?
 
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Read the owner's manual.
 
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Without loss of generality, consider the object to be at rest. Move two test masses close to it on either side and measure their acceleration.
 
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jbriggs444 said:
Without loss of generality, consider the object to be at rest. Move two test masses close to it on either side and measure their acceleration.
could you please be more elaborate
 
Thejas15101998 said:
could you please be more elaborate
About which part?
 
jbriggs444 said:
About which part?
the second sentence
 
Do you know Newton's universal law of gravitation?
 
jbriggs444 said:
Do you know Newton's universal law of gravitation?
yes
 
Thejas15101998 said:
yes
Perhaps you have noticed that the formula has two mass terms appearing within?
 
  • #10
jbriggs444 said:
Perhaps you have noticed that the formula has two mass terms appearing within?
yes, but then?
 
  • #11
Thejas15101998 said:
yes, but then?
Sorry, you are going to have to show some effort here. Take Newton's law of universal gravitation and solve for M. What's on the right hand side?
 
  • #12
GMm/rsquare
 
  • #13
jbriggs444 said:
Sorry, you are going to have to show some effort here. Take Newton's law of universal gravitation and solve for M. What's on the right hand side?
I am not able to comprehend of what you do with finding the acceleration...and wouldn't the accelerations be same for both the test masses when they are close to the rest mass?
 
  • #14
Thejas15101998 said:
GMm/rsquare
Please quote Newton's universal law of gravitation in full. Do not leave out the F. Solve for M.
 
  • #15
Thejas15101998 said:
I am not able to comprehend of what you do with finding the acceleration...and wouldn't the accelerations be same for both the test masses when they are close to the rest mass?
The point of having two test masses is so that they have no net effect on the motion of the mass that you do not wish to affect. Yes, the magnitude of their accelerations would be the same. But would their accelerations be the same regardless of the size of the mass that we wish to evaluate?
 
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  • #16
Thejas15101998 said:
I am not able to comprehend of what you do with finding the acceleration...and wouldn't the accelerations be same for both the test masses when they are close to the rest mass?

An object with larger mass will accelerate the other test masses more, because it has a "stronger" gravity.
 
  • #17
Catch up with it. Match velocity with it. Go into orbit around it at a known distance. Measure the period of the orbit. Find the mass from Newton's form of Kepler's Third Law.
 
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  • #18
Yes, but this will change the velocity of the body.
So the question is pretty much asking to measure some quantity for a system without any alteration in the state of the system.
Which will mean without interacting with the system.
You need to allow for some amount of change, if you want to measure something. In classical mechanics we assume that we can make this change as small as we want. But it is not zero for any real experiment.

In your case, if the probe mass is much smaller than the mass of the moving body, the change in its velocity will be small.
 
  • #19
You can team up with someone else who will approach the planet from the opposite side, such that the distances are always the same, so that the other person's motion is the mirror image of yours in the reference frame of the planet.
 
  • #20
Jenab2 said:
You can team up with someone else who will approach the planet from the opposite side, such that the distances are always the same, so that the other person's motion is the mirror image of yours in the reference frame of the planet.

jbriggs gave the answer. You put an object left, another identical object right, the objects both pull it equally, so its velocity doesn't change, but you can measure how much they accelerate towards the body.
 
  • #21
Thejas15101998 said:
A object is moving in free space with a constant velocity. How will you find the mass of the object without changing its velocity ?
Is this question for your schoolwork?
 
  • #22
berkeman said:
Is this question for your schoolwork?
no...my friend it was just a hot discussion which i wanted to spread.
 
  • #23
With such a succint question, a just correct answer is: it's not possible. Heisenberg dixit.
 
  • #24
The experiment that has been suggested seems ok but it gives the mass of the object in question provided you the identical mass of test objects.
 
  • #25
Let'sthink said:
The experiment that has been suggested seems ok but it gives the mass of the object in question provided you the identical mass of test objects.
You could also use light beams and measure how much they will be bent.
 
  • #26
I appreciate that
 
  • #27
Let'sthink said:
The experiment that has been suggested seems ok but it gives the mass of the object in question provided you the identical mass of test objects.
Why do you think that the mass of the test objects is important?
 
  • #28
I am not just saying that the identical mass, m of test objects is important but that you must know m to find M of the given object.In other words you find M in terms of m.
 

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