Solving a Term about gravitation to r

In summary, the equation provided is used to solve for r. The solution for r is r= ^3√γMeT^2/4Π^2 and this involves multiplying both sides of the original equation by r^2 and then solving for r.
  • #1
wiegetz
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0

Homework Statement


I want to know how this equation is getting solved to r. I know the result, but I want to know how :)

Homework Equations


γ*m*Me/r = 4Π2*m*r/T^2Solution does need to be: r = ^3√γMeT^2/4Π^2 (^3√ should mean the 3rd root/radical)

The Attempt at a Solution


I am so far:
γ*m*Me/r^2 = 4Π2*m*r/T^2 ( shortening the terms now)
γ*Me/r = 4Π2/T^2
γ*Me*/T^2/r*Π2 = 0

Now I do not know how to continue, I am 99% sure that I have done something wrong.
Greetings from Germany! :)

Here is a picture about the term: http://[url=http://postimg.org/image/war0n6zxf/][ATTACH=full]200042[/ATTACH] [ATTACH=full]200043[/ATTACH]
 

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  • #2
wiegetz said:

Homework Statement


I want to know how this equation is getting solved to r. I know the result, but I want to know how :)

Homework Equations


γ*m*Me/r = 4Π2*m*r/T^2Solution does need to be: r = ^3√γMeT^2/4Π^2 (^3√ should mean the 3rd root/radical)

The Attempt at a Solution


I am so far:
γ * m * Me / r2 = 4π2 * m * r / T2 ( shortening the terms now)

The equation above seems to be the one taken from your text.
γ*Me/r = 4Π2/T^2
γ*Me*/T^2/r*Π2 = 0

You canceled the variable r incorrectly. You should have multiplied both sides of the original equation by r2.

After that, leave r3 one one side of the equation and move everything else to the other side. Solve for r.

This is just simple algebraic manipulation.
 
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Likes wiegetz
  • #3
I understood it now. Thanks for the help! :smile:
 

1. How do you solve a term about gravitation to r?

To solve a term about gravitation to r, you will need to use the gravitational equation: F = G * (m1 * m2) / r^2. Rearrange the equation to solve for r, where r is the distance between the two masses m1 and m2. You will also need to know the values for G (gravitational constant) and the masses of the objects.

2. What is the gravitational constant (G)?

The gravitational constant (G) is a fundamental physical constant that is used to calculate the strength of the gravitational force between two objects. It is denoted by the letter G and has a value of 6.674 x 10^-11 N*m^2/kg^2.

3. How do you determine the masses of the objects (m1 and m2) in the gravitational equation?

The masses of the objects (m1 and m2) can be determined by measuring their respective weights (force due to gravity) and the acceleration due to gravity at the location of the objects. Then, using the equation F = m * a, you can solve for the mass (m) of each object.

4. Can the gravitational equation be used for any two objects in the universe?

Yes, the gravitational equation can be used for any two objects in the universe, as long as their masses and the distance between them are known. However, it is important to note that the equation is most accurate for objects that are relatively small compared to the size of the universe.

5. What is the significance of solving a term about gravitation to r?

Solving a term about gravitation to r allows us to calculate the distance between two objects based on their masses and the gravitational force between them. This can be useful in many areas of science, such as astronomy and astrophysics, where understanding the distances between celestial objects is crucial for studying their movements and interactions.

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