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etotheipi

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In summary, the overall change in field strength when both the mass and radius are changed by small amounts at the same time can be found by simply summing the changes caused by each individual change. This can be further explained by considering the small cross terms in the Taylor series expansion and the ability to change mass through physical means such as solar wind or radiation. It is also important to note that this theory can be verified through experimentation, where changing the mass would require running the experiment again with a different mass.

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etotheipi

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etotheipi said:

If you make two small changes, then the overall change is the sum of those changes.

You could look at this a little more rigorously by using a taylor series expansion. The cross terms in ##dMdR## will be small compared to the linear terms in ##dM## and ##dR##.

- #3

etotheipi

PeroK said:If you make two small changes, then the overall change is the sum of those changes.

You could look at this a little more rigorously by using a taylor series expansion. The cross terms in ##dMdR## will be small compared to the linear terms in ##dM## and ##dR##.

I just had a go replacing M and R with [itex]M + dM[/itex] and [itex]R + dR[/itex] and then worked out the resulting change, and ended up obtaining that result you stated with ##dMdR##. Thanks!

- #4

Henryk

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hmm, how do you (physically) change mass? (other than purely mathematically)

- #5

Ibix

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Solar wind, or just radiation. I believe that some stars occasionally emit shells if matter fir one reason or another (you'd be better asking in Astronomy and Astrophysics for details). As long as the mass distribution remains spherically symmetric then when a shell of mass passes your radius, its gravity no longer affects you (look up the Shell Theorem).Henryk said:hmm, how do you (physically) change mass? (other than purely mathematically)

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Henryk said:hmm, how do you (physically) change mass? (other than purely mathematically)

You don't necessarily need to change the mass. You might simply want to look at the effect of small variations in mass (to consider experimental error, for example) on the result of your calculations.

- #7

Henryk

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Ok, that's different.PeroK said:You don't necessarily need to change the mass. You might simply want to look at the effect of small variations in mass (to consider experimental error, for example) on the result of your calculations.

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sophiecentaur

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All this theory relates to experiments that could verify it. Changing the mass would mean running the experiment again with a different mass. Quite acceptable.Henryk said:hmm, how do you (physically) change mass? (other than purely mathematically)

When two variables are incremented at the same time, the resulting change in field strength depends on the relationship between the two variables. If they are directly proportional, increasing both variables will result in a greater increase in field strength. If they are inversely proportional, increasing both variables will result in a smaller increase in field strength.

Yes, if the two variables are inversely proportional, increasing both at the same time can result in a decrease in field strength. This is because as one variable increases, the other decreases, leading to a smaller overall change in field strength.

The rate of change in one variable can have a significant impact on the field strength when the other variable is also changing. A higher rate of change in one variable can result in a greater change in field strength, while a lower rate of change can result in a smaller change in field strength.

The formula for calculating the change in field strength when two variables are incremented at the same time depends on the specific relationship between the two variables. It is important to understand the nature of the relationship (direct or inverse proportionality) in order to accurately calculate the change in field strength.

The effect of increasing both variables on the overall field strength can be determined by analyzing the relationship between the variables. If they are directly proportional, increasing both will result in a greater overall increase in field strength. If they are inversely proportional, increasing both will result in a smaller overall increase in field strength. It is also important to consider the individual rates of change in each variable.

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