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The Hill sphere is a common model for the calculation of a gravitational sphere of influence. It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical body ( m ) in which it dominates over the gravitational influence of other bodies, particularly a primary ( M ). [ 1 ]
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid-shaped region where a particular celestial body exerts the main gravitational influence on an orbiting object. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as moons , despite the ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
Table: Create a table the headers of which specify what the units are, then a table row, then this template, with |cells=y, as the content of the table row (the template creates cells, it doesn't go in one). If a conversion is required, it could be provided in an additional cell, in a column for that unit, e.g. with:
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Hill sphere; Hubble–Reynolds law; Hubble's law; I.
Again, if the mass of the smaller object (M 2) is much smaller than the mass of the larger object (M 1) then L 2 is at approximately the radius of the Hill sphere, given by: The same remarks about tidal influence and apparent size apply as for the L 1 point.
An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2], when t is very small compared to r (). The total surface area of the spherical shell is .
Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius a and the second of radius b (both of height /) and a sphere of radius /. The curved surface area of the spherical zone—which excludes the top and bottom bases—is given by =.