Why exactly do we need the gravitational constant?

[Keith Koenig]

That may seem like a silly question, but suppose the crew of an interstellar vessel wanted to measure the mass of their ship, perhaps to estimate remaining resources. Unless they have very well calibrated thrust and a very well calibrated accelerometer, the only option is to do so gravitationally.

The most likely procedure would be to release a small test mass from the end of a long rod and measure its acceleration a toward the center of mass of the ship at a known distance R from the center of mass, or equivalently time the distance to travel a known distance from a known starting distance and do the math to effectively determine a at R. We know from Newton's law of gravity that regardless of the distance R at which they measure a, the product of a and the square of R has the same value, and that value uniquely identifies the mass of the ship.

What is the likelihood that if this crew is not from earth, they would convert this value from its natural units of length cubed per time squared to some other made-up thing like the "shrock", which is based for example on the density of methane? They might have a name for one unit of length cubed per unit of time squared, but why exactly do we earthlings mask the natural units of mass by dividing by G, the gravitational constant?

That's an honest question. One I don't think we have considered in a very long time.

 

[Nugatory]

but why exactly do we earthlings mask the natural units of mass by dividing by G, the gravitational constant?

We do not always do that.
We do when (for example) we're measuring distances in meters, times in seconds, and want to compare the measured mass with a known mass stated in kilograms. And although your hypothetical non-Terran astronauts are unlikely to use those particular units, they will surely be using instruments that are manufactured and calibrated in whatever units they naturally use on their home world so they will find it convenient to use the appropriate value of ##G##.
On the other hand, when we do not need the immediate comparison with the kilogram or other standard mass unit we routinely choose to set ##G=1##.

 

[anorlunda]

The most likely procedure

How about a procedure that would work on the same principle as a mass spectrometer?

 

[Dale]

but why exactly do we earthlings mask the natural units of mass by dividing by G, the gravitational constant?

We use SI units instead of natural units because they are convenient.

Although ## c=1## is natural, it is inconvenient for municipal speed limits and wind and so forth. In all natural unit systems you wind up with at least some inconvenient unit sizes for human-scale measurements.

The SI is sized to be reasonable for trade and other human endeavors. This is done knowingly and deliberately, despite the unnaturalness.

 

[Keith Koenig]

How about a procedure that would work on the same principle as a mass spectrometer?

View attachment 297988

I like it! But what are the units on the readout? kg? g? I would bet a month's pay they are not ##m^3/s^2##.

 

[Keith Koenig]

We do not always do that.
We do when (for example) we're measuring distances in meters, times in seconds, and want to compare the measured mass with a known mass stated in kilograms. And although your hypothetical non-Terran astronauts are unlikely to use those particular units, they will surely be using instruments that are manufactured and calibrated in whatever units they naturally use on their home world so they will find it convenient to use the appropriate value of ##G##.
On the other hand, when we do not need the immediate comparison with the kilogram or other standard mass unit we routinely choose to set ##G=1##.

My point is there is no need to use anything other than ##G##. Forgive the lengthy post but my wife asked me to explain my point using a T.V. show. This was my reply:

Tony Beets and Parker Schnabel are crew members of the aforementioned hypothetical interstellar ship, and work in a very large cargo hold, which is near the center of the ship and has no artificial gravity. Tony has filled one shipping container with Styrofoam, and a second with gold. Each sits on a pedestal. Tony bets Parker that he cannot guess which one has the gold. Parker may walk up to each container but he is not allowed to lift either one. Lifting a shipping container filled with gold in zero gravity would be no more difficult than pushing the same container sideways on Earth while it is suspended from a crane.

Parker, knowing that mass is more than just "difficulty to move" or "how much there is" takes the bet. He walks in between the two, equidistant from both, removes a gold nugget from his pocket, suspends it perfectly in mid-air, then walks away and waits. He comes back later and determines which container it has moved towards. That one has the gold.

I would bet 2-weeks pay that you have been taught to convert Newtons to ##kg## x ##m/s^2## and back. This emphasizes the fact that the unit of force comes from mass and acceleration. I would up the bet to a month's pay that you have not been taught to convert kg to and from ##m^3/s^2##. This masks the gravitational nature of matter, and I think is not a good thing.

 

[Nugatory]

I would bet 2-weeks pay that you have been taught to convert Newtons to kg x m/s2 and back. This emphasizes the fact that the unit of force comes from mass and acceleration. I would up the bet to a month's pay that you have not been taught to convert kg to and from m3/s2. This masks the gravitational nature of matter, and I think is not a good thing.

You would lose both those bets, and if you were to try them on people you meet in a university physics building your best odds will be the second bet, with the guy you see carrying a mop and pushing around a cart of cleaning supplies.

 

[Keith Koenig]

You would lose both those bets, and if you were to try them on people you meet in a university physics building your best odds will be the second bet, with the guy you see carrying a mop and pushing around a cart of cleaning supplies.

Wait, seriously? Can you cite a textbook that directly converts kg to ##m^3/s^2## and back, not as part of the solution of an equation, but directly. Like in a conversion table between English and Metric. I'm pretty sure that will be a difficult search

[Mentors' note: a digression into a personal theory in violation of the forum rules has been removed]

 

[Ibix]

Wait, seriously? Can you cite a textbook that directly converts kg to ##m^3/s^2## and back, not as part of the solution of an equation, but directly.

Schutz, A First Course in General Relativity uses the ##G=1## convention - see table 8.1. The classic Misner Thorne and Wheeler does as well. Wald's General Relativity too. Carroll's lecture notes don't, though. That's 75% of the textbooks on gravity that I possess...

##G=1## is not as universal as ##c=1## but it's not at all uncommon.

 

[PeroK]

... Hartle's Introduction to GR gives the Schwarzschild metric first in SI units, then in natural units with ##G = c = 1##, which are used for the rest of chapter 9.

 

[PeroK]

I would bet 2-weeks pay that you have been taught to convert Newtons to ##kg## x ##m/s^2## and back. This emphasizes the fact that the unit of force comes from mass and acceleration. I would up the bet to a month's pay that you have not been taught to convert kg to and from ##m^3/s^2##. This masks the gravitational nature of matter, and I think is not a good thing.

In this calculation I used the mass of the Sun as ##1.5 km##:

https://www.physicsforums.com/threa...into-a-black-hole.1012103/page-3#post-6599003

Can I PM you with my bank details?

 

[Nugatory]

A somewhat lengthy digression has been removed from this thread.

The question in the title has been answered, so this thread is closed.