Interactive orbits
You are going to return to the interactive application you have already used, which shows the mathematical model of the motion of a star and planet orbiting around their centre of mass. You are now going to look at it from a different perspective.
Activity 4 Interactive orbits
You have already seen a different view of this interactive application. When it appeared in Section 3.5 you saw a two-dimensional (2D) view looking down on the orbits from above. Now you are seeing a three-dimensional (3D) view, as if you were looking down on the orbit from an inclined view. Consequently the orbital path of the planet appears foreshortened, just as any circle does when you view it like this.
You can change your viewpoint of the orbital plane – the pale red grid in which the orbits lie – by clicking anywhere on it, holding down the mouse button and moving your mouse around (by ‘clicking and dragging’).
Set the mass of the star to 0.3 MSun, the mass of the planet to about 10 MJ and the distance of the planet from the centre of mass to about 4.5 AU.
- Take the fourth slider, which controls simulated time, to the value 0, and then move it slowly to the value 1. As before, you can also use the arrow keys on the keyboard to amend the values. Watch the planet.
Describe the motion of the planet.
Answer
The planet starts off on the axis that is initially pointing towards the right-hand side of the application, and moves anticlockwise all the way around the foreshortened circle, returning to its original position on the axis when t = 1.
- Take the fourth slider back to the value 0, and then move it slowly to the value 1 again. Watch the star this time.
Describe the motion of the star.
Answer
The star starts off slightly to the left of this same axis and moves anticlockwise all the way around the small foreshortened circle, returning to its original position when t = 1. Because the orbit is so small, the star’s motion looks like a small wobble.
From this viewpoint, does the star move towards and away from you during its orbital motion? You may find it helpful to adjust the zoom to focus on the star’s orbital path.
Answer
Yes. The star gets closer to you as it travels from the furthest point on the foreshortened circle, and travels away from you as it moves from the closest point back towards the furthest point.
The velocity of a star as it follows its orbit is independent of the angle you happen to view it from. The star doesn’t care whether or not it is being watched. However, all astronomers can measure is the radial velocity – that is to say the star’s motion towards or away from you. The unknown viewing angle limits what we know about almost all of the planets discovered by the radial velocity method.