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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.

3

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 ...

0

A great amount of planetary data is available at this NASA website. There doesn't appear to be a strong correlation, but you could use this NASA data to do the statistics.

5

To a first approximation the spacetime curvature around the Sun is indeed spherically symmetric. I say to a first approximation because the masses of the planets (particularly Jupiter) also produce curvature and this breaks the spherical symmetry. However let's ignore this for now because I don't think it's relevant to your question. If I understand you ...

1

For systems involving central forces, the orbit can be any of the conic sections. And which conic it will be is determined by the total energy of objects revolving around the centre of force. If the total energy is negative ( as in the case of planets), the eccentricity of the orbit will be either zero or one. If eccentricity is equal to zero, it will be a ...

-3

Comets are coming from almost infinite distance towards Sun. Due to Sun's Gravitational force they should be pulled into Sun rather than forming Elliptical or Hyperbolic trajectory. If object is starting travel from closer distance at considerable speed, we can visualize formation of Elliptical orbit. For object coming from infinite distance getting ...

2

On a planet with gravitation ten times stronger than that of Earth's, will an object fall faster? Yes. It will have ten times greater acceleration. If it starts out at the same height as on earth it will be going faster when it hits the ground and it will hit the ground in less time. If I drop two apples about 8000 meters away from the surface ...

0

Just as there is a Gauss's Law for the Electric Field, there is similarly a law for the Gravitational Field. It states the following: $$-4\pi GM_{enclosed} = \oint \! g \cdot(dA)$$ When you go deeper into the earth, since the mass enclosed by a sphere of a certain radius is directly proportional to the volume enclosed (assuming constant ...

0

Because as you go down, the mass above you has a gravitational pull on you that resists the pull of the mass below you. This continues until you reach the center and the pulls all cancel out, making you weightless. When you go up, the force of gravity on you decrease because of the equation $$F = G\frac{m_1m_2}{r^2}.$$ As the distance increases, its square ...

0

This is due Newtons shell theorem which says that for the particle $m$ all the mass outside the blue shell of radius $r_1$ cancels out: while the mass inside a shell of radius=0 equals also 0 so there is no gravitational acceleration in the gravitational center of the earth (or any planet).

2

Consider this. I have an Earth-sized quantity of water that I throw into space. Naturally, it will assume the shape of a ball. Only if it is non-rotating and is not being influenced by a tidal field. So is there some sort of simple formula that ties these two properties together? Yes. It is called the equation of hydrostatic equlibrium.  ...

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