Keplers laws of motion - quick question on units

AI Thread Summary
The discussion centers on a question about the units in Kepler's law formula for calculating the radius of an orbit. The user is confused about how to derive the radius in meters when plugging in the values for time (T in seconds), gravitational constant (G), and mass (M in kilograms). It is clarified that G refers to the gravitational constant, which has units of m^3/(kg*s^2), not the acceleration due to gravity (g). This distinction resolves the unit cancellation issue, confirming that the equation is indeed correct. Understanding the correct units for G is essential for obtaining the radius in the desired measurement.
channel1
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Homework Statement


find the radius
R3=((T2GM/(4∏2))1/3


The Attempt at a Solution


simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?
 
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channel1 said:

Homework Statement


find the radius
R3=((T2GM/(4∏2))1/3


The Attempt at a Solution


simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?

Homework Statement




Homework Equations





The Attempt at a Solution


G in this problem isn't an acceleration. It's the gravitational constant G. The units are m^3/(kg*s^2).
 
channel1 said:

Homework Statement


find the radius
R3=((T2GM/(4∏2))1/3

The Attempt at a Solution


simple enough, my only question is when I plug in T (units: sec) G (units: m/s^2) and M (units: kg) there is nothing to cancel out the kg so my R is not in units of meters...the equation is correct because we were given it in class but what's going on with the units?

Homework Statement


That's G, not g :wink:

EDIT: Beaten to the punch!
 
Ah hah! Thank you both!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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