Calculating Earth's Orbital Speed: Gravitational Field Equations

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SUMMARY

The discussion centers on calculating Earth's orbital speed using gravitational field equations. The correct formula is v² = GM_sun/r, where G is the gravitational constant (6.67x10^-11), M_sun is the mass of the Sun, and r is the radius of Earth's orbit (1.49x10^11 meters). The initial calculation mistakenly used Earth's mass (5.98x10^24 kg) instead of the Sun's mass, leading to an incorrect speed of 51.7 m/s. The accurate orbital speed of Earth is approximately 29,700 m/s.

PREREQUISITES
  • Understanding of gravitational force and orbital mechanics
  • Familiarity with the gravitational constant (G = 6.67x10^-11 N(m/kg)²)
  • Knowledge of mass values, specifically the mass of the Sun (1.989x10^30 kg)
  • Basic algebra for manipulating equations and calculating square roots
NEXT STEPS
  • Study the derivation of Kepler's laws of planetary motion
  • Learn about gravitational force calculations in different celestial contexts
  • Explore the concept of centripetal force in circular motion
  • Investigate the effects of gravitational interactions on orbital dynamics
USEFUL FOR

Astronomy students, physics enthusiasts, and educators seeking to deepen their understanding of gravitational dynamics and orbital mechanics.

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Homework Statement


It can be assumed that the Earth, to a good approximation, moves in a circular orbit about the sun. Determine the speed of the Earth.

Homework Equations


v2 = GMearth/r

The Attempt at a Solution


mearth= 5.98x1024
R of Earth's orbit= 1.49x1011
G= 6.67x10-11

v2= (6.67x10-11)(5.98x1024)/ (1.49x1011)
v2= (3.98x1014) / (1.49x1011)
v= \sqrt{}2676.9
v= 51.7m/s

Now here's the problem. My teacher said that the answer to this question is 2.97x104m/s
What is it that I am doing wrong? D:
 
Physics news on Phys.org
The important mass, the one that the Earth orbits, is the mass of the Sun.
 
Ohhhh. Okay, I got it. Thank you
 

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