Unit Conversion (mass, radius )

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SUMMARY

The discussion focuses on calculating the radius of a newly discovered planet with a mass approximately 5.5 times that of Earth and a density equivalent to Neptune's density of 1.76 g/cm³. The initial attempt incorrectly applied the density formula, leading to confusion. The correct approach involves using the volume formula for a sphere, resulting in a final radius of 16,500 kilometers. This highlights the importance of accurately applying the density equation D = M/V in astrophysical calculations.

PREREQUISITES
  • Understanding of density calculations (D = M/V)
  • Familiarity with the volume formula for spheres
  • Basic knowledge of planetary mass and radius comparisons
  • Ability to convert units between kilograms and kilometers
NEXT STEPS
  • Learn how to calculate the volume of a sphere using the formula V = (4/3)πr³
  • Explore the properties of planetary densities and their implications for composition
  • Study the methods for determining exoplanet characteristics from observational data
  • Investigate the relationship between mass, radius, and density in astrophysics
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in planetary science and exoplanet research will benefit from this discussion.

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Homework Statement



In January 2006, astronomers reported the discovery of a planet comparable in size to the Earth orbiting another star and having a mass of about 5.5 times the Earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. Take mass Earth 5.97 x 10 ^24 and radius Earth 6.38x10^6.

If this planet has the same density as Neptune (1.76 g/cm^3), what is its radius expressed in kilometers?

What is its radius expressed as a multiple of Earth's radius?

Homework Equations



D=MV

The Attempt at a Solution




My attempt:

I got (5.97x10^24kg Earth's mass / 6380 km Earth's radius) x (.00176 kg mass of unknown planet mass / x the radius of the unknown planet)

= 1.068676422 x 10^-21

The answer does not seems right, I did convert each unit accordingly.

Please and thank you in advance.
 
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Well for one thing, density is M/V, not M*V. I don't understand what you are doing. Where's your use of the density equation?
 
Nevermind, I solved it using the formula for finding the volume of sphere. In which it lead me to the final radius of 1.65 x 10 ^4 km.

Thank you anyways. :wink:


I just noticed the mistake of the D=M/V formula I stated before, can't believe I did that.
 

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