Average speed of earth in its orbit of sun

In summary, the Earth's orbit around the sun has an average radius of 1.5x10^11 m and an average speed of 29.29 km/s. Ramanujan's approximation of the circumference of an ellipse was used to calculate the orbital velocity, which contradicts the answer provided in the book.
  • #1
bilbobaggins
12
0

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
 
Last edited:
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  • #2
Your t value is a little off. Can you explain how you got it?

Hmm, I get the same answer you do though.
 
Last edited:
  • #3
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.
 
  • #5
Try calculating it yourself! I'm inclined to believe the book's answer is wrong.
 
  • #6
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,

[tex]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)[/tex]

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.)
 

1. What is the average speed of Earth in its orbit around the sun?

The average speed of Earth in its orbit around the sun is approximately 67,000 miles per hour or 107,000 kilometers per hour.

2. How long does it take for Earth to complete one orbit around the sun?

It takes Earth approximately 365.24 days, or one year, to complete one orbit around the sun.

3. Does the speed of Earth in its orbit around the sun stay constant?

No, the speed of Earth in its orbit around the sun varies slightly due to factors such as gravitational pull from other planets and the sun, and changes in Earth's distance from the sun.

4. What is the significance of the average speed of Earth in its orbit around the sun?

The average speed of Earth in its orbit around the sun is important in determining the length of a year and the changing seasons on Earth. It also helps scientists understand the gravitational forces at play in our solar system.

5. How does the average speed of Earth in its orbit around the sun compare to other planets?

Earth's average speed in its orbit around the sun is faster than the outer planets (such as Neptune and Uranus), but slower than the inner planets (such as Mercury and Venus). However, all planets have varying speeds in their orbits due to their distance from the sun and gravitational pull from other bodies in the solar system.

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