Planet X Has Free Fall Acceleration

[Anthony]

ThePlanet I'm speaking of has the same size as earth but is much lighter. That's because the "Upper Mantle" is about 1000 km wider and mostly consist out of organic material. Such a huge mass of carbon on one planet isn't very realistic but I need it to have an excuse for lower gravity on the surface.Picture from Wikipedia

I haven't put much thought in the moon neither. The Moon is supposed to be close and big enough to affect the habits of animals on the surface by lowering their "Free-fall acceleration". (big enough difference for them to orient themselves on it) As an example: In these phases some of them would be hunting because it needs them less energy.

I answered this question (How to get periodic low gravity) by positing a binary planet. If Earth were a moon of Jupiter, in the orbit now occupied by the actual Jovian moon Metis, Jupiter overhead would effectively decrease weight on things on Earth by 30%.

I am delighted by this prospect but can understand that you might have problems with a Jupiter sized chunk of uranium being your world's moon. You could make this more reasonable by bringing the dense moon into a tighter orbit than our moon is, and so it would be closer (as in the linked Metis example) where a Jupiter sized chunk of Jupiter stuff can accomplish the same pull as a Jupiter sized chunk of uranium at Luna distance. Or you could assert your moon is made of superdense matter - maybe the stuff of neutron stars, or the theoretical superheavy elements which start at about 3 times the mass of uranium.

This means that any body in the Universe feels the gravity of any other body in the Universe. So the crow which is now in my garden is attracted by the Andromeda Galaxy millions of light years away. BUT...

Unlike Earth and the Moon, Io's main source of internal heat comes from tidal dissipation rather than radioactive isotope decay [...]. Such heating is dependent on Io's distance from Jupiter, its orbital eccentricity, the composition of its interior, and its physical state. [...] The vertical differences in Io's tidal bulge, between the times Io is at periapsis and apoapsis in its orbit, could be as much as 100 m.

The gravitational force of the Moon on a human walking on Earth is close to zero because the Moon attracts not only the human, but also the Earth; while the human is indeed falling towards the Moon with a certain acceleration, Earth is falling towards the Moon too with just about the same acceleration, and thus the net effect on the human relative to Earth is almost zero. Look at the nice picture:

A human walking on Earth falls towards the Moon with an acceleration just a tiny little higher than the acceleration with which Earth itself falls towards the Moon. The mass of the human is assumed to be negligible with respect to the masses of the Earth and the Moon. Own work, available on Flickr under the CC Attribution license.

$$a_\textH-M - a_\textE-M = G \cdot m_\textMoon \frac 2d_\textE-Mr_\textE - r^2_\textEd^2_\textE-M(d_\textE-M - r_\textE)^2 \simeq G \cdot m_\textMoon \frac2r_\textEd^3_\textE-M$$

We notice that the relative acceleration of the human with respect to Earth is just about proportional with the radius of the Earth and inversely proportional with the cube of the distance between the Earth and the Moon. (The approximation holds if the radius of Earth is small with respect to the distance between Earth and the Moon.)

One of the ways that planets end up with rings is that another smaller (or with lower surface gravity) celestial body comes close enough to it that the planets gravity exceeds the other body's gravity at its surface ripping it apart. So, if you want to have tides significantly effect gravity then you have to look for a system where the planet is approaching the limit for how close it could reach the moon without being destroyed by it. Now in reality that Roche limit does not exist because the smaller body would be ripped apart first. As a result if you want want a planet with significant fluctuation in free-fall acceleration due to tidal forces of another celestial body then you would probably be looking at something a lot closer to a binary system or a system where your "planet" is actually the moon than an earth/luna system.

What you're talking about is "gravitational tidal effects". Our Moon raises tides on Earth in the same way you're planet's satellite does. Most people know about the ocean tides, but there are also "Earth tides": The surface of the Earth moves up and down about 1/3 of a meter.

Over the longer term, the resulting "tidal acceleration" effect (a bit of a misnomer) slows down the planetary rotation and speeds up the satellite's orbit, until they end up being tide-locked as our Moon is now.

It's hard to estimate the speed of this process for your world without more information on its geology. If there's a sensible effect (maybe 10% of normal gravity? More?), and if your planet's mass and moment of inertia are smaller (to give smaller g), this is going to be geologically fast: The planet's rotation will slow to match the satellite's orbit period, and the variations will disappear.

First, the distance at which the satellite can provide a meaningful improvement in a jump is perilously close to the point where the world begins to break up as the satellite's tidal forces overwhelm the planet's cohesion due to its own gravity.

Second, "So what?" you say. Just set up the satellite's orbit far enough away not to disrupt the planet by close enough to allow for a 10% local diminution of effective gravity. But those enormous tidal forces are going to raise tremendous tides, not only in the planet's oceans but in the solid rock. And this will release vast amounts of heat. Interestingly, that heat started out as the energy of rotation of the planet. (If the planet and satellite mass anything like Earth, and the planet rotates in 24 hours, the satellite would probably have to be inside geosynch to raise a 10% tide, so the effect of the tides would be to steal the planet's rotational energy to drive the satellite out and slow the planet's rotation down. Eventually, there'd be a stable situation where the planet and the satellite were tidelocked to each other. At this point, the energy loss from tides would greatly diminish.

Finally, long before that happened, the tides themselves would have renderedthe planet uninhabitable. The rock tides would be tens or hundred of miles high, would completely disrupt the planet's surface, probably melt it, and certainly stir up massive volcanic activity to saturate the rubble in lava. Io on steroids!

In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies;[1] the measurement and analysis of these rates is known as gravimetry.

At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation.[2][3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft/s2),[4] depending on altitude, latitude, and longitude. A conventional standard value is defined exactly as 9.80665 m/s (about 32.1740 ft/s). Locations of significant variation from this value are known as gravity anomalies. This does not take into account other effects, such as buoyancy or drag.

Newton's law of universal gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is:

where M \displaystyle M is the mass of the field source (larger), and r ^ \displaystyle \mathbf \hat r is a unit vector directed from the field source to the sample (smaller) mass. The negative sign indicates that the force is attractive (points backward, toward the source).

Here g \displaystyle \mathbf g is the frictionless, free-fall acceleration sustained by the sampling mass m \displaystyle m under the attraction of the gravitational source.It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends only on how massive the field source M \displaystyle M is and on the distance 'r' to the sample mass m \displaystyle m . It does not depend on the magnitude of the small sample mass.

This model represents the "far-field" gravitational acceleration associated with a massive body. When the dimensions of a body are not trivial compared to the distances of interest, the principle of superposition can be used for differential masses for an assumed density distribution throughout the body in order to get a more detailed model of the "near-field" gravitational acceleration. For satellites in orbit, the far-field model is sufficient for rough calculations of altitude versus period, but not for precision estimation of future location after multiple orbits.

The more detailed models include (among other things) the bulging at the equator for the Earth, and irregular mass concentrations (due to meteor impacts) for the Moon. The Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 consists of two probes, nicknamed "Tom" and "Jerry", in polar orbit around the Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth, and to track changes that occur over time. Similarly, the Gravity Recovery and Interior Laboratory mission from 2011 to 2012 consisted of two probes ("Ebb" and "Flow") in polar orbit around the Moon to more precisely determine the gravitational field for future navigational purposes, and to infer information about the Moon's physical makeup.

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