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

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SUMMARY

Changing a planet's radius directly affects its mass when assuming uniform density. If a planet's radius is one-fifth that of Earth's (6.38 * 106 meters), its volume is calculated using the formula for the volume of a sphere, V = (4/3)πr3. Given Earth's mass of 5.97 * 1024 kg, the mass of the smaller planet can be determined by calculating the volume ratio and applying it to Earth's mass, resulting in a mass of approximately 0.008 kg if the density remains constant.

PREREQUISITES
  • Understanding of the formula for the volume of a sphere
  • Basic knowledge of density (density = mass/volume)
  • Familiarity with Earth's mass and radius
  • Ability to perform ratio calculations
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  • Study the formula for the volume of a sphere in detail
  • Learn about density and its implications in astrophysics
  • Explore the relationship between volume and mass in planetary science
  • Investigate how varying density affects planetary mass calculations
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Students studying physics or astronomy, educators teaching planetary science, and anyone interested in understanding the relationship between a planet's radius and mass.

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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?
 

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