How close can a planet with an elliptical orbit get to another planet?

Question

I am writing about a fictional cluster of different solar systems and in one of them I created a planet that harboured life. I wanted to make it a bit more interesting and came up with the idea that there existed a planet with an elliptical orbit in the same system that would sometimes perfectly align with the other planet filled with life affecting the gravity with it's own. I was thinking that this would become like a season were all the creatures could suddenly jump higher and I have already thought out how they would evolve in reaction to this sudden change in gravity that would come in seasons. But now I'm wondering if this is even possible. I have imagined them to both be of earth like size and I am unsure if this is even realistic.

My question is. How close can this elliptical planet fly by the other without getting pulled into each other or screwing up each others orbit and still preferably have some gravitational change for the life forms on the planet?

Answer 1

You probably would need a moon

You apparently want to have a situation that would cause people on one side of your planet to feel less gravity than normal at specific times. This cannot be done with a flyby planet. The reason is that whatever gravitating mass there is pulls all the other masses towards itself, thus anything in the sky would pull both people and the planet, with force difference reversely proportional to cube of distance to that mass divided by planet radius. So, the Sun, even being quite heavy vs the Earth, does very minimal gravity difference on the surface, because it's very far. Thus, in order to have another celestial body to influence gravity on your planet, you need a moon.

The planet's moon

Imagine Earth having its Moon being about six times closer to Earth than it is in reality (9 radii of Earth, or 57330 km away from surface, on a circular orbit with radius of 10 radii of Earth, or 63700 km). This change would make people on the side that's facing the Moon to be pulled towards the Moon with acceleration of 6.67e-11*3.347e22/5.733e7^2 = 6.792e-4 m/s^2, but the Earth would be pulled towards the Moon with acceleration of 5.502e-4 m/s^2, making the difference of gravity to equal 1.29e-4 m/s^2. The Earth's gravity is 9.81 m/s^2, so even if the Moon would be at 10 Earth radii orbit, it would only make people on Earth lighter by 1.31e-5 fraction, or 1.31e-3 percent. This is way not enough to make people jump higher by a visible margin.

But actually, even with our Moon located at its original distance, there are quite a lot of effects from Moon's gravity influence. Tides, for example, are the most prominent, but there are also some effects against Earth's crust and mantle, which are of about the same magnitude (12 km of crust vs 6370 km of radius - too small difference to notice here). But with Moon placed this close, all the effects would be marginally stronger, about 200x stronger, mind you! (6^3=216) Thus, tides would on average be 14 times larger (sqrt(200)), any forces applied to crust will be 200x higher, this would make Earth a lot more inhospitable. If you would plan to have a planet fly by, the effects would be marginalized even more, to the extent of a high tide wave flooding cities or valleys - this would be more visible than "people can jump a bit higher".

The planet IS a moon

Another possibility is to make your planet a moon of some gas giant, which would be large enough to create such disturbances of gravity on the planet's surface. But then your planet has to be outside the gas giant's Roche limit (for the planet, this limit also depends on the planet's mass) in order for it to stay whole. There would be a lot of tidal effects on that planet from the gas giant's gravity, which will quickly make the planet tidally locked, aka facing the gas giant with one side. Provided you will find the exact numbers that would make the planet's orbital period be small enough to count as a "long day" and the giant to be located in the star's habitable zone, this configuration can possibly provide your people with "seasons", yet there will be two areas with lower gravity than on the rest of the planet, one directly under the gas giant and the other on the opposite side of the planet. You can still postulate that the planet still maintains relative spin to the gas giant, as if the tidal locking hadn't fully happened, creating your high jump seasons, but remember that there will be also high tides.

Answer 2

It's not gonna work.

Jupiter's moon Io is covered in volcanoes, with tides 20,000 times stronger than Earth's. Not just kangaroos jump higher - the rock of the moon itself rises 100 meters, creating friction that leads to its unique appearance.

Now what's the actual change of gravity on Io? I'm afraid I have to go back to first principles, but here's the template I stole the math code from. With

$G=6.67430 \cdot 10^{-17} N⋅km^2⋅kg^{−2}$

$m_j=1.898 \cdot 10^{27} kg$

$R_0=420~000~km$, $R_1=423~400~km$

$r_i=1~821~km$ $$ a_{min} = G\frac{m_j}{(R_1+r_i)^2} \approx 0.701 \frac{m}{s^2}\\ a_{max} = G\frac{m_j}{(R_0-r_i)^2} \approx 0.724 \frac{m}{s^2}\\ \Delta a \approx 0.024 \frac{m}{s^2} $$

Now on this infernal landscape of Io, this calculation yields that the gravity changes by about 1/500 Earth "gee". In the process, the rock of the moon rises by 100 meters (which is still much less than 1/500 of 1821 km, presumably due to inertia and the friction that heats the moon). Nonetheless, you're not going to feel anything dramatically different.

Now formally the question is about how close the worlds can come together, which depends mostly on the Roche limit. I don't have data to work with for your specific case but you can use the article to get an idea. The orbital mechanics can be arranged in various ways (orbital resonance or a switching of orbits comparable to Epimetheus and Janus. It can still be an astronomical delight, with "interesting" geological consequences.