Finding the mass of a planet using gravitational acceleration and radius

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SUMMARY

The mass of Planet Z, with a diameter of 5000 km and a free-fall acceleration of 7.00 m/s², can be calculated using Newton's law of gravitation. The formula applied is g = GM/R², where g is the gravitational acceleration, G is the gravitational constant, M is the mass of the planet, and R is the radius. By rearranging the equation and substituting the known values, the mass of Planet Z can be derived accurately. The gravitational constant used in the calculations is 6.674 × 10⁻¹¹ N(m/kg)².

PREREQUISITES
  • Understanding of Newton's law of gravitation
  • Familiarity with gravitational acceleration concepts
  • Knowledge of unit conversions, particularly between kilometers and meters
  • Basic algebra for rearranging equations
NEXT STEPS
  • Learn about the gravitational constant (G) and its applications in astrophysics
  • Study the derivation of gravitational acceleration formulas
  • Explore unit conversion techniques for scientific calculations
  • Investigate the relationship between mass, radius, and gravitational force in planetary science
USEFUL FOR

Students in physics or astronomy, educators teaching gravitational concepts, and anyone interested in planetary mass calculations.

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Homework Statement



Planet Z is 5000 km in diameter. The free-fall acceleration on Planet Z is 7.00 m/s^2. What is the mass of Planet Z?

Homework Equations



Well Newton's gravitational law G(M1M2)/R^2
And I cannot think of much else


The Attempt at a Solution



On one of the earlier homeworks we were given a table in which there were fictional planets and their ratios of mass and radius to Earth so I tried using

gG M(earth)/(R(earth))^2 = gG M(z)/(R(z))^2
Where the "g"s are each planet's free fall acceleration.
so that the Gravitational constant would cancel and I'd have the Mass of planet Z

For the mass of the Earth I used 5.97E34, for the radius of the Earth I used 6387.1 km
I know that the radius needs to be in meters and would be correctly notated as 6.3871E6

I don't know how to figure this one out
 
Physics news on Phys.org
Welcome to PF.

F = ma = GMm/r2

a = GM/r2
 
Thank you very much
 

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