Calculating Earth's Orbital Speed: Gravitational Field Equations

AI Thread Summary
The discussion centers on calculating Earth's orbital speed around the Sun using gravitational field equations. The initial calculation incorrectly used Earth's mass instead of the Sun's mass, leading to a significant error in the speed result. The correct formula requires substituting the mass of the Sun, which is crucial for accurate calculations. The final correct speed of Earth in its orbit is approximately 29,700 m/s. This highlights the importance of using the correct celestial body mass in gravitational calculations.
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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:
 
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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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