Sorry, the title's length didn't allow me to explain this better and I need it for a story that I'm writing, if you're so kind to help me. I've been trying it hard to solve it myself but I've been unable to.(adsbygoogle = window.adsbygoogle || []).push({});

The problem looks simple but it isn't (for me): Please assume we have a space probe of negligible mass in a highly eccentric, heliocentric polar orbit (so it doesn't experience heavy perturbation caused by other solar system bodies; let's say it "goes up and down" the Sun.) I need this probe to "meet" (experience a close encounter with) the Earth twice every time it travels along the perihelion (i.e. 6 months of travel between each extreme of the Sun-focus latum rectum), like in this drawing:

Could anyone please help me to solve the following:?

Thank you in advance for any help! (And please move if this is not the appropriate forum...)

- Dimensions of the ellipse (major and minor axis and/or eccentricity);
- Total orbital period;
- Maximum velocity at the perihelion; and, most important:
- Velocity (relative to the Earth) while "crossing" the Earth's orbit "upwards" and, 6 months later, "downwards."

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# Heliocentric polar orbit crossing the Earth's orbit twice

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