# What is Earth's linear velocity around the Sun?

I am creating a theoretical model of the Earth's tangential acceleration around the Sun (on an elliptical orbit, not circular). First, I will build a theoretical model, which is not influenced by any other planet or mass in the solar system, and then compare it to the actual data available.

For this I would require data on the actual linear velocity of Earth around the Sun (using my method), does anyone know how I can obtain this data?

• Between ~29 and ~30 km/s is it's speed... Oct 4 at 21:34

You can obtain this data (and other solar system data) to high accuracy using the HORIZONS software by NASA.

Use the following settings:

• Ephemeris Type: VECTORS
• Target Body: Earth [Geocenter] [399]
• Coordinate Origin: Sun (body center) [500@10]

This will generate the position and velocity of Earth relative to the Sun at the specified time(s). More settings can be adjusted using Table Settings.

• @noob anomaly, also note that you might want the velocity of Earth relative to the Sun-Earth system, which is slightly different from it relative to the Sun (the Sun has a slight wobble because of the Earth's orbit). Aug 29 at 9:56

You can use the vis-viva equation, the derivation is available on wikipedia, you can easily get it there. It uses the conservation of angular momentum. I'm stating the equation here.

$$v^2 = GM(\frac{2}{r}-\frac{1}{a})$$

Here, $$a$$ is the semi major axis, and $$r$$ is your distance.

Hope this helps.