Graviational acceleration given mass and radius

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SUMMARY

The gravitational acceleration on a planet with five times the mass of Earth and twice its radius can be calculated using the formula GM/r². Given that the mass of Earth is 6.00 x 1024 kg and its radius is 6.38 x 103 km, the gravitational acceleration at the surface of the new planet is determined to be 12.25 m/s². Key to solving this problem is ensuring all units are in SI and applying the gravitational constant correctly. The discussion emphasizes the importance of unit consistency and strategic problem-solving approaches in physics.

PREREQUISITES
  • Understanding of gravitational force and the formula GM/r²
  • Familiarity with SI units for mass and distance
  • Basic knowledge of physics problem-solving techniques
  • Ability to convert units (e.g., kilometers to meters)
NEXT STEPS
  • Study the derivation of gravitational acceleration using GM/r²
  • Learn about unit conversions in physics, particularly for mass and distance
  • Explore gravitational constants and their applications in different celestial contexts
  • Practice solving physics problems involving gravitational forces with varying mass and radius
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in understanding gravitational acceleration calculations in astrophysics.

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Homework Statement


If you lived on a planet with five times the mass of Earth and twice the radius, what would be the gravitational acceleration at the surface of your planet?


Homework Equations


GM/r^2
Mass of Earth = 6.00*10^24 kg
Radius of Earth = 6.38*10^3 km

The Attempt at a Solution


So, when I started out doing this, I quickly plugged in Earth's radius (in m), mass (in kg) and the gravitational constant just to make sure it came out at 9.8 because I know that's what Earth's gravitational acceleration from the surface is, but none of the answer I get are even close. I can't even get this right and I still have to do the actual problem (using 5x the mass and 2x the radius).
 
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Two rules for doing physics problems:
1 - Check your units
2 - Never put in a hard number until you can't avoid it

You're tripping over rule 1 - which of your numbers is not in SI units?

Remember rule 2 when you're doing the question proper. The approach I suspect you are about to use will work, but there is a way to do it without needing to know either the Earth's mass or radius.
 
Thanks, I actually went back and redid it later and got the answer I was looking for.
 

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