questions

Discussion in 'Astronomy, Exobiology, & Cosmology' started by Oniw17, Sep 9, 2007.

  1. Oniw17 ascetic, sage, diogenes, bum? Valued Senior Member

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    3,423
    How do you calculate the path a natural satelite will take to orbit an object? Also, how do you do the math for a star system like alpha centauri(actually I only want to know about a binary system)? Also, how can you tell the gravity of an object?...and does the gravity of a star affect stars close to it if they're not part of a system?
     
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  3. mathman Valued Senior Member

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    The basic method of calculation is using the law of gravity. In the cases you mention, Newton's law would be accurate enough. Gravitational effect is infinite, but it dies off with the square of the distance between the objects involved.
     
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  5. orcot Valued Senior Member

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    3,488
    Is that yust a saying our is this for real.


    First you have to now the distance between the object (how high the orbit is) then you also have to have the mass of the main body the Mass of the secundairy body can be ignored when at best it's yust a few tons against
    E-24 kg of earth.

    Note the less difference between the two objects or other influence the more circular your orbit gets

    maybe this link wil also help
     
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  7. Janus58 Valued Senior Member

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    2,394
    First, you need to know the mass of the object being orbited, and then you need to know the distance of the satellite from the object, its mass, and its velocity (both speed and direction) at some point of its orbit.
    From this you can find the total energy of the satellite from:

    (1) E= mv²/2-GMm/r
    where
    M = mass of object
    m = mass of satellite
    v = scalar value of the satellite's velocity (speed only)
    G =gravitational constant of the universe.
    r = center to center distance between object and satellite.
    (Note: if the total energy comes out as a positive value, the satellite is moving faster than escape velocity and will not orbit the object but will fly off into space.)
    The total energy can also be found by:

    (2) E = - GMm/(2a)

    where
    a = the semi-major axis of the orbit or average orbital distance of the satellite.

    By equating equations 1 and 2 and solving for a we can find the semi-major axis of the orbit.

    With that we can find the period(P) of the orbit:

    (3)P = 2pi sqrt(r³/(GM))


    Next we need to find the eccentricity(the degree of how elliptical the orbit is) of the orbit.

    To do this we first find the areal velocity for the satellite.

    We find this by
    (4) A = rv sin(o)/2
    where
    o = the angle between the direction of the satellite's motion and the line joining the satellite and the object.

    and

    (5) A = pi(a²)sqrt((1-e²))/P

    Equate equations 4 and 5 and solve for e, the eccentricity.

    With this information we can find the periapis(r_p) and apapsis(r_a), which are the closest and furthest point of the orbit from the main object.

    (6)r_p = a(1-e)
    (if this value is less than the radius of the obect being orbited, then the satellite will crash into its surface.)

    (7)r_a = a(1+e)

    We can also find the satellites distance from the object at any point of its orbit by

    (8) r = a(1=e²)/(e cos(f)+1)

    where
    f = the true anomaly = the angle between the the satellite's position and the periapsis as measured from the center of the object being orbited. which allows us to plot out the orbit.

    The above assumes that the satellite is very small when compared to the object being orbited. In a binary system, where the two objects are closer in mass to each other, things change. and adjustments have to be made. For instance, the equation for the period changes to

    (3.1)P = 2pi sqrt(r³/G(M+m))
    You can determine the gravity of an object by observing the objects that orbit it. With stars, there is a relationship between the luminousity and the mass of the star. brighter stars are more massive.

    The effect the individual stars have on each other is very very small and can be ignored. As a group however, the combined effect is what holds galaxies togehter.
     
    Last edited: Sep 11, 2007

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