- #1
xpell
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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.
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:?
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:?
- 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."