Orbital speed variation as a planet orbits the Sun

In summary, Kepler's law can be used to calculate the orbital speed at a given distance from the sun.
  • #1
tempack
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Summary:: At what distance from the Sun will the speed of the planet be equal to the average orbital speed?

I'm not sure where to place this question, please move it in the right thread.

[Mentor Note -- thread moved from the technical forums, so no Homework Template is shown]

At what distance "r" from the sun will the speed of the planet be equal to the average orbital speed? If it is possible, I need a formula, where the Perimeter of the ellipsoid is not involved as a parameter. If you have a link with more details, then even better.

Great thnx
 
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  • #2
tempack said:
Summary:: At what distance from the Sun will the speed of the planet be equal to the average orbital speed?

I'm not sure where to place this question, please move it in the right thread.At what distance "r" from the sun will the speed of the planet be equal to the average orbital speed? If it is possible, I need a formula, where the Perimeter of the ellipsoid is not involved as a parameter. If you have a link with more details, then even better.

Great thnx
Can't you just get that from Kepler's laws and conservation of energy?

Except, of course, the perimeter of an ellipse is not so easy to calculate. What's the relevance of average speed?
 
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  • #3
tempack said:
At what distance "r" from the sun will the speed of the planet be equal to the average orbital speed?
Just to be clear, you mean its own mean orbital speed? Wikipedia quotes (without derivation, unfortunately, but with a reference) a series for the mean orbital speed and an exact expression for orbital speed as a function of radius.
 
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  • #4
The total energy of the orbiting system is ##E = -\frac{GMm}{2a}## (for a quick way in, look at the Virial theorem), and we have$$ -\frac{GMm}{2a} = \frac{1}{2}mv^2 - \frac{GMm}{r}$$That gives you the Vis-viva equation$$v = \sqrt{GM \left (\frac{2}{r} - \frac{1}{a} \right)}$$I don't know how to calculate the perimeter of an ellipse but if someone more clever knows how to do that then you can just divide by ##\frac{2\pi}{\sqrt{GM}}a^{\frac{3}{2}}##.

Maybe there is a better way that avoids having to approximate the perimeter :wink:
 
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  • #5
Sorry for my english, I'm using google translator.
I understand so:
Mean orbital speed Vm=P/T, where P - perimeter, T - Perioud. For my problem I need Vm=Vi, where Vi - instantaneous orbital speed

I need an alternative way to get "r", by ex from Kepler's law.

PS: There I'm nub...
 
  • #6
Sorry, "Perimeter" = ellipse circumference
"Perioud"= orbital perioud
@etotheipi, thnx for your answer, but this method I know. I need an other way
 

Related to Orbital speed variation as a planet orbits the Sun

What is orbital speed variation?

Orbital speed variation is the change in speed of a planet as it orbits the Sun. This variation is caused by the varying distance between the planet and the Sun throughout its orbit.

What causes orbital speed variation?

The elliptical shape of a planet's orbit around the Sun causes orbital speed variation. As the planet moves closer to the Sun, it speeds up due to the increased gravitational pull. As it moves further away, it slows down due to the decreased gravitational pull.

How does orbital speed variation affect a planet's orbit?

Orbital speed variation affects a planet's orbit by causing it to move at different speeds at different points in its orbit. This can impact the length of a year, as well as the planet's position in relation to the other planets in the solar system.

Can orbital speed variation be measured?

Yes, orbital speed variation can be measured using mathematical equations and observations of a planet's position and velocity at different points in its orbit. This information can also be used to make predictions about future orbital speed variations.

How does orbital speed variation impact the overall motion of a planet?

Orbital speed variation impacts the overall motion of a planet by causing it to move in an elliptical path around the Sun. This variation also contributes to the planet's overall speed and direction of movement in relation to the Sun and other celestial bodies in the solar system.

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