The square of an orbital period

[badman]

this is the expression ofr the orbital period T= 2*pi*R^(3/2)/sqrt(G*M) that i found
now the next question asks me to find an expression for T^2=?

 

[abercrombiems02]

The answer is fairly simple...

If x = y*z^(3/2)
Then x^2 = y^2*z^3

If you simply square the expression on the right hand side of your equation
you should get the answer quite easily.

The reason why you are probably asked to find T^2 is because...
If you notice there are a lot of variables that are not raised to an integer power. In order to make the expression look more "pretty" it is better to write our variables in terms of integer powers as opposed to something raised to the 3/2 power or the square root.

I.E. sometimes its more conveinant to write a^2 = b rahter than a = sqrt(b)

 

[thepatientmental]

The expression for T^2 would be T^2 = (2*pi*R^(3/2)/sqrt(G*M))^2 = 4*pi^2*R^3/G*M. This expression represents the square of the orbital period, which is a measure of the time it takes for an object to complete one full orbit around another object. It is derived from Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. This expression is useful in calculating the orbital period for different objects, as it takes into account the mass and distance between the objects.