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3

Even though you were wrong, you nailed the critical question at the heart of the necessary understanding. Bold is my emphasis: Modelling this planet at my head then anywhere that effective gravity increases in strength is effectively lower potential energy "down" from anywhere that it doesn't. I would expect this to cause the planet to deform and reshape ...


1

Your intuition is correct. At that scale, the planet behaves essentially like a liquid, and it's shape will equalize into an ellipsoid where: The local gravity vector is everywhere perpendicular to the surface, and The downward force felt by a person standing on the surface is the same everywhere. But I don't think you could get an eccentricity as ...


0

If it's a hyperbola, the semi-vertical angle is half the angle between the asymptotes and the cutting angle of the cone is parallel to the axis of the cone. Otherwise, it's not unique. There's an infinite number of pairs of angles that would yield the same conic section. Edit: Nevermind. You can get hyperbolas at more than one set of angles too.


2

No, the Earth's gravity varies over its surface because (a) the Earth is not spherical, (b) it does not have a uniform (or spherically symmetric) distribution of density and (c) of course the "surface" is at different heights. You can find a local gravitational strength (and direction - because the local gravitational vector does not necessarily point to ...


0

No, acceleration due to gravity varies, depending solely on the altitude on which Gravitational force is working, the approximate* value can be determined using equations: g(eff, h) = g*[(r/r h)^2] H being the altitude, r being earth's mean radius, g effective is the acceleration due to gravity at an altitude h above sea level. Thanks :) Approximate because ...


4

If the Earth were a perfect sphere, it would be the same everywhere on Earth's surface. This is known as the shell theorem. It's not too hard to show mathematically, but you can think of it as the fact that all the mass that is close to you balances roughly with the mass that is far away. If you were to tunnel into the Earth, however, you would only ...


1

There is plenty of evidence for planets around evolved stars (giants) and there is also plenty of evidence for planetary material around white dwarfs and planets around neutron stars. Planets around red giants are primarily found using the Doppler technique (the planets are too small compared with the star to produce a significant transit signal). See for ...


2

For your first question, a requirement for a solar system is that there must be at least one star contained within it. Without a star or some other intense gravity field holding the planets in orbit, the planets would drift away. It is possible for any class of star- from dwarf to supergiant- to hold planets in orbit and therefore have a solar system. ...


1

A presentation on the SETI Weekly Seminar series (available on Youtube) points out that tidal locking (e.g. expected of a planet in the habitable zone of a red dwarf) can involve higher muliples than same-face-shows, and in fact an eccentric orbit favors an odd half multiple (3:2 like Mercury). There is also orbital inclination to consider. The pattern of ...


2

In general the acceleration of gravity at the surface of a planet depends on both its radius and its mass (density times volume): $$g=\frac{GM}{R^2}= \frac43\pi G\rho R$$ For a given amount of work done by the athlete ($F\Delta x$), height jumped scales roughly with $g$. A vertical jump looks like this: From a standing start you jump up and measure ...


-1

Figure out a planet in orbit of 360 degree. You would have a 45 degree axis at start and -45 degree axis at mid course of this planet around the orbit. It would means that this planet would have taken a speed or inclined throughout that course implying that from Her own, it developed a way to tilt like around an ice cream cone. This could means that a ...


2

For a conventional planet (i.e. one that is self gravitationally round), conservation of the planet's angular momentum makes this impossible (except for the trivial case of the axis perpendicular to the orbital plane. A non-spherical planet with a tilted axis will precess under the influence of tidal forces. It takes the earth about 26,000 years to go ...


1

Start digging at the equator and move all the dirt to the polar regions. This will decrease the moment of inertia of the planet about its spinning axis. Due to the conservation of angular momentum this will result in an increase in angular velocity, akin to a figure skater who retracts her arms while spinning.


2

Cover it in mirrors that are highly reflective on one side and painted black on the other. Position the mirrors so that the "faces" are perpendicular to the surface. A sketch is below (I have only shown three mirrors, the idea is that you would cover the planet with them, but they will be most effectively placed close to the equator). The plan is that each ...



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