Computational Physics - Scaling

[secret2]

Hi all,

I am not sure if I'm posting on the right place. I am currently working on a computational project. It's about simulating a system with two non-test masses and a bunch of test masses. The instruction sheet says that we should "scale the problem carefully by setting the units such that the non-test masses have a mass of 1 and G, the universal gravitation constant, equals 1."

The lecturer did a bad job explaining what scaling really is, and I am not sure what exactly I should do concerning scaling here. Could someone give me a hand?

 

[HallsofIvy]

What you write doesn't make a whole lot of sense. If you had one mass, you could certainly choose ITS mass as the "unit of mass" and so it would have mass 1- you would then "scale" by dividing all other masses by the "unit" mass.

However, if you have "two non-test masses", unless they are both the same mass, obviously you can't have both with mass 1.


Once you have selected a given unit of mass, setting G (I presume you don't mean "g") equal to 1 is a matter of choosing an appropriate distance measure.

 

[secret2]

HallsofIvy,

Thank you for your help, I have been desperately looking for reply.

First of all, you are right that the two non-test masses have equal masses. I am not sure why you commented that "obviously you can't have both with mass 1".

And after having selected a given unit of mass, setting G equal to 1 is "a matter of choosing an appropriate distance measure" as you mentioned. To be explicit, I have two questions:

1. Do I need to 'scale' both distance and time?
2. Is it true that I have to divide distance by the sqrt of G in order to scale it?

Many thanks!

 

[HallsofIvy]

You said you had two "non-test masses". You didn't say they were the same. What exactly IS a "non-test mass"??
G has units of \frac{m^3}{(kg)(sec^2)} Yes, you will need to scale all of them. The point is choosing each of those so that G is 1.

 

[secret2]

When I said 'test mass' I mean that they will not exert any gravitational attraction onto the other test/non-test masses (they of course REACT to the attraction of the non-test masses). So you can say that there are only two sources of gravitational attraction.

Cheers