How Does Changing a Planet's Radius Affect Its Mass?

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Changing a planet's radius affects its mass based on the volume and density relationship. If a planet's radius is one-fifth that of Earth, its volume is significantly reduced, calculated using the formula for the volume of a sphere. Assuming the same density as Earth, the mass can be determined by multiplying the volume ratio by Earth's mass. The discussion emphasizes understanding the density formula, where density equals mass divided by volume. The key takeaway is that mass is not directly proportional to radius but is influenced by volume and density.
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Homework Statement



I know this is a dumb question but if the radius of a planet is one-fifth of the Earth's radius. what is the mass of the planet.

Earth mass => 5.97 *1024
earth radius => 6.38 *106

The Attempt at a Solution



my answer: 5.97 *1024(1/10)
 
Last edited:
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unseenoi said:

Homework Statement



I know this is a dumb question but if the radius of a planet is one-fifth of the Earth . what is the mass of the planet.

Earth mass => 5.97 *1024
earth radius => 6.38 *106

The Attempt at a Solution



my answer: 5.97 *1024(1/10)

And incorrect.

If the radius is 1/5 and it has the same density as earth, then what would the mass be?

Think about the ratio of the volume between the 2 and then multiply that appropriately by Earth mass.
 
Can u please give me more details.
 
density = mass/volume --> \rho=m/v

What is the formula for determining the volume of a sphere? Given the Earth's radius, what is its volume?
 
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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