If I jump up and down, am I literally making the earth oscillate on its orbit? I guess the answer to this depends on whether the planet’s particles, on average, are experiencing an acceleration enough to move them more than the planck length?
Regardless though, there must be some cutoff. Or is the planck length so small that two protons at opposite ends of the observable universe are repelled on this scale (once photons actually arrive)?
Is the earth’s surface inelastic? I don’t think so, but I’m no expert.
I thought about that, but it shouldn’t matter. Obviously the main effect of my motion is just deforming or vibrating the ground immediately where I land.
However, my gravity should also be affecting all the particles everywhere; this is true even before I land.
I’ll admit I cheated and used ChatGPT to help with the math, but it appears as though the deflection of you jumping, while incredibly small, is still many orders of magnitude greater than the plank length.
how much force is imparted to the earth by a human jumping?
ChatGPT
The force imparted to the Earth by a human jumping is typically very small and negligible in comparison to the Earth’s mass. When a person jumps, they exert an upward force on the Earth, and by Newton’s third law of motion, the Earth exerts an equal and opposite force on the person. However, due to the significant difference in mass between a human and the Earth, the resulting force on the Earth is extremely tiny.
To illustrate this, let’s consider an example. Suppose a person weighs 70 kilograms and jumps with an upward acceleration of 2 meters per second squared. Using Newton’s second law of motion (force = mass × acceleration), the force exerted by the person would be:
Force = mass × acceleration Force = 70 kg × 2 m/s² Force = 140 Newtons
However, this force is distributed over the area of contact between the person’s feet and the ground, which is relatively small. As a result, the pressure applied to the Earth’s surface is very low.
To put it into perspective, the Earth’s mass is approximately 5.97 × 10^24 kilograms, so the force exerted by a human jumping is negligible compared to the Earth’s mass. The impact of a single human jumping does not have any significant effect on the motion or behavior of the Earth.
how much is the earth moved by this?
ChatGPT
The displacement of the Earth caused by a human jumping is practically undetectable due to the vast difference in mass between the Earth and a human. While the Earth does experience a reaction force when a person jumps, it is important to consider the scale of the Earth’s mass, which is approximately 5.97 × 10^24 kilograms.
Even if we assume an unrealistically high force of 1000 Newtons (which is well beyond what an average human can generate), the resulting displacement of the Earth can be calculated using Newton’s second law of motion:
Force = mass × acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Force / mass
Acceleration = 1000 N / 5.97 × 10^24 kg
Acceleration ≈ 1.67 × 10^-22 m/s²
Using this acceleration, we can calculate the displacement of the Earth using the equation:
Displacement = 0.5 × acceleration × time²
Assuming a time of 1 second, the displacement would be:
Displacement = 0.5 × 1.67 × 10^-22 m/s² × (1 s)²
Displacement ≈ 8.35 × 10^-23 meters
and Plank length ≈ 1.616255(18)×10^−35
Elasticity may figure in and reduce the displacement a bit, but the Plank length is very small.
Ok. But does that mean there will be any measurable movement in one particular direction after all the interactions between the rather large number of particles in the universe?
Measurable in practice? No.
Measurable by Laplace’s Demon, with a measuring tape billions of light years long with Plank length graduations and the ability to calculate out all those other particle’s effects? Sure.
To a reasonable degree of approximation, unless you can achieve escape velocity, you will come back down and, therefore, not change the centre of mass of the Earth by leaving the system. Definitely not as much as the massive earthquakes and other effects that deform the planet (slightly affecting its orbit); you will have to worry about those first to figure out what jumping up and down may do.
ETA a related question is that, in principle, all those gravitational sling manouevres used by spacecraft should slightly knock the planets involved around…
It depends how fat you are. 
About half as big as yo momma 