Why, when the planet is accelerated during the ‘close phase’ of its orbit, isn’t it then flung away? I get that gravity pulls/holds it in orbit but why hasn’t it flattened out into a spherical orbit?
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> Why, when the planet is accelerated during the ‘close phase’ of its orbit, isn’t it then flung away?
It is. That’s how it gets to the “far phase” of its orbit. At which point it’s decelerated, and “falls back down” into the “close phase” of its orbit. (In technical terms, the faster speed near periapsis helps the orbiting object get back to apoapsis and the slower speeds near apoapsis cause it to fall back to periapsis.)
> I get that gravity pulls/holds it in orbit but why hasn’t it flattened out into a spherical orbit?
There’s no force acting to do so, at least not in the idealized case we’re talking about. And a force that isn’t just the central pull of gravity is required to change an orbit.
To make an orbit more circular, you need to thrust (EDITED, had these backwards) ~~*forward*~~ *backward* (~~prograde~~ retrograde) at your closest point in the orbit (periapsis) or thrust ~~*backward*~~ *forward* (~~retrograde~~ prograde) at your most distant point in the orbit (apoapsis). This thrust is perpendicular to the pull of gravity, so gravity can never supply it, at least not in the idealized case we’re talking about. Some other force, like the pull of another object or the thrust of a rocket, is needed to do so.
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