Notice : If you wish to know how to make an oscillating orbit with real-world physics, you can looky-look at this question which is following mine. My question focuses on the consequences of such orbit.
A wavy stellar system
I have a stellar system with quite unique properties. How this system has come to be is unknown, but its central body -which for sweetness we'll call a white-hole- has unique physical properties. It gives out a force similar to gravity but acting as the reverse of it with a "higher derivative strength" : By this mathematical word abomination, I mean it decreases faster over distance than gravity does. In other words, if you're close, you get pushed away, and if you're far, you get pulled in. As a consequence, there is a sphere/circle where you are in a state of weightlessness, where the gravity's force counteract the repulsing one. Later on, we'll call this line the neutral-line.
Around this white-hole stands a telluric planet, quite similar to Mars in terms of composition and orbital characteristics, excepted for one thing. Due to some yet-to-understand space history, its orbit is crossing 8 times the neutral-line, as it is oscillating from and to the pull-zone with contrary forces. It forms a pretty star-like shape, as you can see in the toy model I made1 below :
The red planet's orbit forming a star-like shape around the white star-like body.
My issue
This model, however, doesn't help me solve the fact that planets have got lots of added complexity, notably regarding their structure. They're not "solid as rock" like pétanque balls (or bowling ones if you're more accoustumed to them).
So what can I expect the structure of such planet to be, relatively to Mars? Here, I ask :
- Its general shape? An oval, a pancake (yummy!), exactly like Mars, something else?
- Would there be visible structure changes over-time at its surface when seen from another planet? Like signs of very strong pressures which leads to cracks, volcanic and seismic activity?
- And as part of a reality-check, would it be structurally obliterated into dust by such oscillations?
Known data from the model
Here are some data I gathered from my model that I guess could be useful in understanding the thing. Although... Recall that it's a toy model with much, much smaller-scale data (we're talking in km, not AUs)! Therefore, I can only reasonably give relative differences, and there might be large scale differences I'm not aware of!
- The speed of the object changes overtime. In my model, it ranges from 1 unit to 2 units of speed, quite a lot if I dare say. As you can see on the image, the speed increases as the object gets nearer the white-hole, and slower as it gets further.
- The force varies over time, too. For 1 N of overall pull force I get at the furthest distance, I get 1.6 N of push back force at the closest one.
- As for the distance, the planet's distance to the white-hole ranges from ~80 to ~140% of the neutral line distance. We'll consider the neutral line distance white-hole to be the same of what Mars would have, so your orbit ranges from 80% to 140% of Mars's orbit.
- For time, well... My model's going over the board and making a loop takes less than 15 minutes, so :D... We'll take in that to make a full period, it's the same as Mars. The thing here is that because it's oscillating along the neutral line, I doubt the third Kepler's law to calculate orbital periods applies here. In fact, by adjusting the perpendicular initial velocity, you get different loop times, as you can see below :
A side-by-side race between two planets with different initial velocity. The yellow planet has half the initial perpendicular speed of the red one, and takes a lot more time to move around
Other data
Outside the model's results, know that the white-hole, apart from its physic changing properties, act like the Sun gravity-wise and energy emission-wise. If by chance you're missing something, consider it to be Mars or Sun-based approprilate... Appropriately.
Therefore, what would be the structural impact a planet would face by having an oscillating orbit?
1 : Here's the model formula, whose result is positive when the object is attracted towards the white hole, and repulsed when negative. I mainly used as a sketch-up, but if you need it :) :
$$ F = -A \frac{m_h m_o}{d_{ho}^{2.5}} + G \frac{m_h m_o}{d_{ho}^2} $$
With F being the force applied, mh the hole's mass, and mo the mass of the repulsattracted object, dho the distance between the hole and the object, G the gravitational constant and A another "convenient" constant to balance things out. I don't really care what's inside the white-hole and didn't want to make general relativity calculations, so dho=0's undetermined result is irrelevant. Same for the white-hole's own movement, which I waived away since it's not really significant.