Quick Guass's Law of Gravitation Clarification

In summary, the conversation is about a question regarding the last step of a sample problem, specifically the equation ∇g = C (1/r^2)∂/∂r(r^4). The person is also confused about the meaning of the symbol "∴". The expert provides a link to explain the first question and a definition of the symbol for the second question.
  • #1
bmb2009
90
0

Homework Statement



The picture attached shows the answer to a sample problem... I don't understand the last step... how does ∇g = C (1/r^2)∂/∂r(r^4) ? where did the r^4 come from and what does the triple dot triangle: "∴" mean? I understand every step except for the last one... thanks

Homework Equations





The Attempt at a Solution

 

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  • #2
bmb2009 said:

Homework Statement



The picture attached shows the answer to a sample problem... I don't understand the last step... how does ∇g = C (1/r^2)∂/∂r(r^4) ? where did the r^4 come from and what does the triple dot triangle: "∴" mean? I understand every step except for the last one... thanks

Homework Equations





The Attempt at a Solution


To answer your first question:

http://en.wikipedia.org/wiki/Divergence#Spherical_coordinates


To answer your second question, this symbol: ##\therefore## means, "therefore."
 
  • #3
ahh thank you so much
 

What is Quick Gauss's Law of Gravitation?

Quick Gauss's Law of Gravitation is a simplified version of the original law of gravitation proposed by the 18th century physicist, Carl Friedrich Gauss. It states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

How is Quick Gauss's Law of Gravitation different from the original law?

The main difference between Quick Gauss's Law of Gravitation and the original law lies in the units used to measure mass and distance. In Quick Gauss's Law, the units are chosen such that the proportionality constant is equal to 1, making calculations simpler and quicker.

Can Quick Gauss's Law of Gravitation be applied to all objects in the universe?

Yes, Quick Gauss's Law of Gravitation can be applied to all objects in the universe, regardless of their size or mass. However, it is most accurate when used to calculate the gravitational force between two large objects, such as planets or stars.

Is Quick Gauss's Law of Gravitation accurate enough for scientific calculations?

Quick Gauss's Law of Gravitation is a simplified version of the original law and is not as accurate. It is often used for quick estimations or calculations where precision is not critical. For more precise calculations, the original law of gravitation should be used.

Are there any limitations to Quick Gauss's Law of Gravitation?

Yes, there are limitations to Quick Gauss's Law of Gravitation. It does not take into account other factors such as the shape and density of the objects, as well as the presence of other objects in the vicinity. It also does not apply to objects that are moving at high speeds or in extreme gravitational fields.

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