An introduction to exoplanets

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# Orbital motion and radial velocity

We are now going to explore how the motions around the centre of mass and the radial velocity are related. In reality all astronomers ‘see’ is a point of light on the sky: the star. The laws of physics, which underly the changes in the light that astronomers collect from the star, allow the real motion of the star and its planet(s) to be determined. Astronomy proceeds by unlocking the information carried by light from objects we are unlikely to ever be able to view up close.

## Activity 7  Orbital motion and radial velocity

This application shows orbital motions in a system where a star is 1500 times more massive than its planet. The separations are scaled so the planet’s orbit just fits on the screen - the planet and star are shown much larger relative to their separation than they would really be. With the initial settings the observer is looking at the system from above and to the right of the orbital plane.

The application shows two animated arrow vectors – light green represents the true velocity of the star. The star’s speed stays the same as it moves around its circular orbit, but its velocity continuously changes direction as shown. Remember, the star and the planet move in opposite directions at each instant. The star moves much more slowly than the planet: in the time that it takes for the planet to move around the big circle, the star moves around a circle that is too small to even be seen in this application. The star’s motion is just a wobble around the centre of mass that is too small to easily discern.

The second animated arrow vector, in orange-brown, shows the radial velocity of the star relative to the distant observer. When the star is moving to the right, the radial velocity arrow points towards the observer, along the purple line. When the star moves to the left, the radial velocity arrow points away from the observer, along the extension of the purple line below the orbital plane. To help you to see this, remember that you can drag the orbital plane around to change your viewpoint.

The application gives the values of the stellar orbital speed (which never changes) and the stellar radial velocity, which changes continuously as the direction of the star’s motion changes continuously as it moves around its orbit.

Active content not displayed. This content requires JavaScript to be enabled.
Interactive feature not available in single page view (see it in standard view).

When the radial velocity is towards the observer (orange-brown arrow aligned along the purple line), is the value of the stellar radial velocity positive or negative?

Negative.

When the radial velocity is away from the observer (orange-brown arrow aligned away from the purple line), is the value of the radial velocity positive or negative? (You can pause the application if you need to.)

Positive.

What is the biggest value the stellar radial velocity ever has with the initial settings? (If necessary, you can refresh the page to reset all of the sliders to the initial settings, i = 77° and aplanet = 14.55.)

10.8 m/s (give or take however much uncertainty your clicking led to).

In what direction is the true velocity of the star pointing when the radial velocity has its maximum value?

To the left, away from the observer, who is to the right and above the orbital plane.

Keeping the application paused at its maximum value of radial velocity, adjust the orbital inclination, i, using the slider. You can also use the arrow keys on the keyboard to amend the values.

For orbital inclination i = 90° exactly, what value does the stellar radial velocity now show? What do you notice about this value?

11.1 m/s. This value is the same as the orbital speed. When the orbit is exactly aligned with the direction to the observer like this, the maximum radial velocity will be the same as the speed because the motion is exactly along the line to the observer.

For orbital inclination i = 30° exactly, or as close as you can get it, what value does the stellar radial velocity now show? What do you notice about this value?

5.56 m/s. This is about half the value obtained at i = 90°.

Even when the observer is looking quite steeply down on the orbit, the radial velocity reaches half the orbital speed.

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