Why does a planet with $v_cNot sure if I worded the question properly, but my question is about an image shown in Your Daily Equation #17 by Brian Greene
He shows the following image:

Where
red is the case $v = v_c$ and
green is the case $v_c < v < v_e$
with $v_c$ meaning the velocity required for circular motion and $v_e$ the escape velocity.
This to me seems strange since the green orbit with a supposedly higher speed approaches the sun more closely than the red orbit with a lower speed.
Is this really how reality works? or is it simply a detailed ignored for the video's sake?
If reality really works this way, could anyone explain to me why it is that the green orbit gets pulled closer to the sun than the red one?
 A: 
Is this really how reality works?

No, this is not how reality works. It is an incorrect representation of reality.  While the green ellipse does appears to be an ellipse, it does not represent an elliptical orbit about the Sun. The incorrectness caught your attention and made you question the presentation. Bad graphics are worse than no graphics at all.
A better representation would have the green ellipse always be outside the red circle except at the one point where the green ellipse and red circle intersect. The closest point on an ellipse to a focus is always on the ellipse's major axis. The closest point on the green ellipse to the Sun is not on the ellipse's major axis. That's because the Sun is not a focus of the green ellipse.
To be true to the shape of the green ellipse, it should have been drawn shifted to the right so that the Sun was at a focus. That would not have helped illustrate the point Brian Greene was trying to make. To be true to the point Brian Greene was trying to illustrate, the green ellipse shouldn't have been so eccentric.
A: Brian Greene apparently does not know how to plot a proper ellipse. The green line should lie between the red and magenta lines.
