Average speed of earth in its orbit of sun

AI Thread Summary
The average speed of Earth in its orbit around the sun is calculated using the formula for circular motion, but there are discrepancies in the expected answer. The initial calculation yielded approximately 29,865.95 m/s, while the correct average speed is stated to be 28,886 m/s. Participants in the discussion noted that the time value used in the calculations might be inaccurate, leading to confusion. One contributor referenced Ramanujan's approximation for elliptical orbits, which resulted in a calculated speed of 29.7838 m/s, suggesting that the textbook answer could be incorrect. Overall, the conversation highlights the importance of accurate data and calculations in determining Earth's orbital speed.
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Homework Statement


The Earth's orbit around the sun is very nearly circular, with an average radius of 1.5x10^11 m. What is the average speed of the Earth in orbit around sun.

Homework Equations



d/t= 2pi/t

The Attempt at a Solution



2pi*1.5x10^11/ 31556926
it comes out to be 29865.95
answer is supposed to be v=28,886 m/s
so can anyone tell me what i did wrong

31556926 is a year so that's why i used it in the equation
 
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Your t value is a little off. Can you explain how you got it?

Hmm, I get the same answer you do though.
 
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hage567 said:
Your t value is a little off. Can you explain how you got it?

Hmm, I get the same answer you do though.

I used google to find t, lol.
 
Try calculating it yourself! I'm inclined to believe the book's answer is wrong.
 
The relevant data are
a=1.00000011 au
e=0.01671022
T=365.242190 days (tropical year)

Using Ramanujan's approximation of the circumference of an ellipse,

C=\pi a \left(3\left(1+\sqrt{1-e^2}\right)-\sqrt{\left(3+\sqrt{1-e^2}\right)\left(1+3\sqrt{1-e^2}\right)}\right)

the Earth's orbital velocity is 0.01720159 au/day, or 29.7838 m/s

From http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html, the Earth's minimum orbital velocity is 29.29 km/s, larger than the supposedly correct answer. (In other words, the book is wrong.)
 
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