Universal gravitation 2- determine the planet's orbital period

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SUMMARY

The discussion centers on calculating a planet's orbital period using the formula T=2π√(R³/GxMs), where R is the total distance from the sun, G is the gravitational constant, and Ms is the mass of the sun. The user correctly identifies the mean distance from the sun as 2.00x10^11 m and incorporates the radius of the sun (Rs=6.96x10^8 m) and the mass of the sun (Ms=1.99x10^30 kg) to find R as 2.007x10^11 m. The calculated orbital period T is approximately 49,034,131.61 seconds. The user seeks clarification on the units for the period, indicating a need for further understanding of unit conversion in physics.

PREREQUISITES
  • Understanding of gravitational physics and orbital mechanics
  • Familiarity with the gravitational constant (G)
  • Knowledge of unit conversion in physics
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Research the gravitational constant (G) and its value (6.674×10^-11 m³ kg^-1 s^-2)
  • Learn about unit conversion techniques in physics, particularly for time
  • Explore Kepler's laws of planetary motion for additional context on orbital periods
  • Study the derivation of the orbital period formula T=2π√(R³/GxMs)
USEFUL FOR

Students studying physics, particularly those focusing on celestial mechanics and orbital dynamics, as well as educators seeking to clarify concepts related to gravitational forces and orbital calculations.

dani123
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Homework Statement



A planet's mean distance from the sun is 2.00x10^11 m. Determine the planet's orbital period. Use information found in textbook.

Homework Equations


So I use the following equations:

R=h+Rs

T=2∏√(R3/GxMs)

From the textbook I got the following values:

Rs=6.96x108m
ms=1.99x1030kg

The Attempt at a Solution



From the problem we also know that h=2x1011m

So with that and the radius of the sun we are able to find the radius that will be used in the orbital period equation. R=(6.96x108m)+(2x1011m)=2.007x1011m

with all these values we plug them into the orbital period equation and solve for T=49034131.61

I don't know how to get the units for the period however... If someone could tell me if my calculations are correct and how I find these units that would be greatly appreciated! Thank you so much in advance for your time and help!
 
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Since you just wrote numerical values for "R", "Rs", h, and "Ms" without saying what any of those mean I don't see how anyone can determine what you are doing much less what the units should be.
 

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