What must the Dimensions of G be for this equation to be dimensionally correct?

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The discussion focuses on determining the dimensions of the gravitational constant G for the escape speed equation to be dimensionally correct. It emphasizes that the escape speed is influenced by G, the mass of the Earth, and the Earth's radius, independent of the escaping object's mass. Additionally, it seeks to establish the values of a and b in the period equation T = 2*π*G^(-1/2)*M^a*r^b for dimensional correctness, where M is the mass of the Sun and r is the distance from the Sun. The participant expresses confusion about the problem's requirements and seeks guidance on understanding the equations involved. Clarity on these concepts is essential for solving the physics problems presented.
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Homework Statement



"An object from the surface of the Earth with the escape speed ve can move infinitely far from the Earth. The escape speed is independent of the mass that is trying to escape and only depends on G, the gravitational constant, ME the mass of the Earth, and RE the radius of the Earth.

a.) What must be the dimensions of G be for this equation to be dimensionally correct?

b.) Given your units for G in part (a), what must the values of a and b be for the equation for T, the period of a planet around the Sun, below to be dimensionally correct?
T = 2*π*G^(-1/2)*M^a*r^b

Here M is the mass of the Sun and r the distance the planet is from the sun. The power of G is already given at -1/2.

Homework Equations



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The Attempt at a Solution



None. This "class" consists of a "textbook" that contains only physics problems and no explanations as to how to do them, and "lessons" that consist only of the teacher writing problems on a white board and us having to solve them in class. I need a full lesson on how to do this, but am clueless as to where to find it, or even what to look for. I'm not even sure what the question is asking.
 
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What's the first equation the problem is referring to?
 

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