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Gravitational Acceleration question

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  • Gravitational Acceleration question

    From my senior high school boy's workbook:

    Black holes are suspected when a visible star is beingt noticeably ulled by an invisible partner that is more than 3 times as massive aas the sun. A) If a red giant (a dying star) is gravitationally accelerated at 0.075m/s (square) toward an object that is 9.4 x 10 (to the tenth power) m away, how large a mass must the unseen body possess? B) How many times more massive is the object than the sun? Where the mass of the sun is: Mass of the sun = 1.99 x 10 (to the 30th power) kg)
    Life is what you make of it...so please read the instructions carefully.

  • #2
    Re: Gravitational Acceleration question

    Aww cmon Craig. You know you can get in trouble for cheating on your homework!

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    • #3
      Re: Gravitational Acceleration question

      Stars have mass? I didn't even know they were Catholic.

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      • #4
        Re: Gravitational Acceleration question

        My physics is kind of rusty and I don't have a physics text book handy but the problem gives initial conditions where the units are meters/sec/sec (or meters/sec (squared) for accleration and meters for distance. From that you need to find an answers who's units is kilograms for mass. Someone needs to find an equation or two that deals with this.

        If I had to start somewhere maybe using the equation Force = Mass x accleration.

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        • #5
          Re: Gravitational Acceleration question

          Originally posted by craigwatanabe View Post
          From my senior high school boy's workbook:

          Black holes are suspected when a visible star is beingt noticeably ulled by an invisible partner that is more than 3 times as massive aas the sun. A) If a red giant (a dying star) is gravitationally accelerated at 0.075m/s (square) toward an object that is 9.4 x 10 (to the tenth power) m away, how large a mass must the unseen body possess? B) How many times more massive is the object than the sun? Where the mass of the sun is: Mass of the sun = 1.99 x 10 (to the 30th power) kg)
          They didn't give you the mass of the red giant? the force of gravitational attraction is dependent on the masses of both objects and is inversely proportional to the distance between their centers.
          Last edited by Mike_Lowery; January 15, 2007, 11:22 AM.
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          • #6
            Re: Gravitational Acceleration question

            Gravitational Acceleration? I remember experiencing that in college...the more beers I drank the faster I'd hit the floor...

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            • #7
              Re: Gravitational Acceleration question

              Originally posted by Mike_Lowery View Post
              They didn't give you the mass of the red giant? the force of gravitational attraction is dependent on the masses of both objects and is inversely proportional to the distance between their centers.
              Correct. The *force* depends on the mass. But since a=F/m, the mass cancels out and the acceleration is independent of the mass of the red star (*IF* one assumes that the mass of the other body is so large that the attraction of the red giant doesn't significantly the black hole.)

              Now what I want to know is if they can't see the black hole, how do they know how far away it is from the Red Giant?

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              • #8
                Re: Gravitational Acceleration question

                Originally posted by Mike_Lowery View Post
                They didn't give you the mass of the red giant? the force of gravitational attraction is dependent on the masses of both objects and is inversely proportional to the distance between their centers.
                I assume because there is a known rate of attraction and that the mass of the sun is given you don't need to know the mass of the Red Dwarf, but I do believe by using ratios you can derive a factor to determine the mass of the Red Dwarf. In order to derive that factor you must have some sort of universal gravitational constant and through the almighty algebraic function apply that constant to your ratio then apply it inversely to determine the unknow mass of the Red Dwarf then to the rate of acceleration.

                It has been wayyyy too long for me to answer this for my high school kid. Thankfully my Freshman older boy who is a math wizard, (some people see dead people, Vance see's formulas) looked at it and figured it out in his head as fast as he could read it.

                Amazing. He can solve time travel but he can't jump start his own car.
                Life is what you make of it...so please read the instructions carefully.

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                • #9
                  Re: Gravitational Acceleration question

                  Brudda Iz was a big star, and he get plenty mass.
                  Burl Burlingame
                  "Art is never finished, only abandoned." -- Leonardo Da Vinci
                  honoluluagonizer.com

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                  • #10
                    Re: Gravitational Acceleration question

                    Originally posted by craigwatanabe View Post
                    Red Dwarf
                    Red Giant. Super Red Giant. Blue Giant. Don't be confusing them with dwarf stars now which are at the other end of the spectrum.
                    "Hey fool, we gots yo leada!"
                    "But I can't even read good."
                    "Whatever that means, you ____ peasant."
                    "That (stuff) is the MOST BALLER THING EVAAA!!!!"

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                    • #11
                      Re: Gravitational Acceleration question

                      Oh I see. I thought you were looking through your old high school books.

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                      • #12
                        Re: Gravitational Acceleration question

                        This is a great thread. A great ending would be for your boy to publish the answer here so we can all ponder a while.

                        I know that I'm curious as ever. No really. I swear I'm not kidding. Honest.

                        I hope the answer looks like something from a cartoon.
                        FutureNewsNetwork.com
                        Energy answers are already here.

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                        • #13
                          Re: Gravitational Acceleration question

                          Well, since on one wants to touch a simple high school question....

                          The formula for gravitational attraction is given by:

                          F=G*m1*m2/r^2
                          where
                          F=force
                          G=Gravitational Constant
                          m1=mass of star
                          m2=mass of black hole

                          Acceleration is given by:
                          F=m1*a
                          F=force
                          m1=mass of star
                          a=acceleration


                          Putting the two formulas together, we get:
                          m1*a = G*m1*m2/r^2

                          Simplifying:
                          a=G*m2/r^2
                          (notice we no longer need to know the mass of the red giant)

                          Solving for mass:
                          a*r^2/G=m2

                          Plugging in the numbers and checking the units:
                          0.075m/(s^2) * (9.4*10^10 m)^2/(6.6742 x 10^-11 m^3 s^-2 kg-1) = 9.9x10^30 kg.

                          Of course, this does assume that the black hole is sufficiently massive that the we can ignore the acceleration of the black hole toward the red giant. Because "a" in the first formula is the acceleration of the two bodies toward each other, not the acceleration of the reg giant toward a fixed point.

                          I'll leave it to the reader to solve the last part of the question with simple division.

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                          • #14
                            Re: Gravitational Acceleration question

                            << with Simpson-like drool hanging dangerously from left side of lip>>

                            "I knew that"
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                            Energy answers are already here.

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                            • #15
                              Re: Gravitational Acceleration question

                              Originally posted by GeckoGeek View Post
                              Of course, this does assume that the black hole is sufficiently massive that the we can ignore the acceleration of the black hole toward the red giant. Because "a" in the first formula is the acceleration of the two bodies toward each other, not the acceleration of the reg giant toward a fixed point.
                              Now that I think about it, my statement above is wrong. Since the force acts on both bodies, it doesn't matter if both move or not. That is, the force on the Red Giant doesn't change if the black hole were somehow held stationary. If the force remains the same, then the acceleration must be the same.

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