Page 1 of 2 12 LastLast
Results 1 to 15 of 19

Math Help - Newton's Law of Gravitation

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    24

    Newton's Law of Gravitation

    So I need some help with this problem:

    Newton's Law of Gravitation states that the magnitude F of force exerted by a body of mass m on a body of mass M is F(r)=(GmM)/r^2, where G is the gravitational constant and r is the distance between the center of the bodies. Suppose that one of the bodies is the earth and the other is a 1000-kg satellite. The earth's mass is approximately 5.98(10^24) kg concentrated at the center and its radius is approximately 6.37(10^6)m. G=6.67(10^-11) N * m^2/kg^2

    a. Determine how fast the force between the earth and satellite changes when the satellite has launched vertically to a height of 1000 km.
    b. Explain the physical meaning of the minus sign for the rate of force with respect to the distance between the bodies.
    c. The determination of work required, when a force and change in distance is given, is analogous to determining the displacement when the velocity and change in time is given or the change in charge when the current and the change in time is given. Compute the work required to launch the satellite vertically to a height of 1000 km.

    I really need some help trying to figure out what I need to do in order to proceed with this problem. Don't want the answers just help solving it

    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    You are given:

    F(r)=\frac{GmM}{r^2}

    a) Differentiate with respect to time t.

    b) As r increases, what happens to F(r).

    c) Use W=\int_{r_1}^{r_2}F(r)\,dr
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    Okay I actually have a question how would I start to differentiate with respect to t?
    Last edited by DjNito; November 19th 2012 at 08:46 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    would I have to do implicit differentiation with dF/dt?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    I would write the function as:

    F(r)=GmMr^{-2}

    Now, use the power and chain rules (recall GmM is a constant).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    okay so I got

    dF/dt = (-2GmM)/r^3 ? is that right? cause I don't think it is in respect to time t
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    You have neglected to apply the chain rule. Your answer would be correct if we are differentiating with respect to r. So, what do you need to add?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    OK I am unsure of what I use the chain rule on.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    Since r is a function of t you want to apply it to r.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    oh got it haha its late lol

    So I got:

    (-2GmM/r^3)(GmM/r^2)

    because t is a function of r so I multiply the derivative by the original function right?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    No, you want to write:

    \frac{d}{dt}(F(r))=-\frac{2GmM}{r^3}\cdot\frac{dr}{dt}
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    Oh I actually had that I just thought since it was a function I had to replace it with the original equation
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    Are you given any information regarding the rate at which the satellite moves upwards?
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Newbie
    Joined
    May 2011
    Posts
    24

    Re: Newton's Law of Gravitation

    no everything I am given is in my original post
    Follow Math Help Forum on Facebook and Google+

  15. #15
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Newton's Law of Gravitation

    Okay, then your result for part a) will have to be a function of dr/dt. Just plug in the given distance from the center of the Earth.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. gravitation question
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: March 23rd 2011, 04:31 PM
  2. gravitation
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 26th 2009, 09:32 AM
  3. A problem os Newton´s law of gravitation
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 11th 2009, 07:30 PM
  4. Newton's Law of Gravitation
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 6th 2008, 03:45 AM
  5. Replies: 4
    Last Post: October 31st 2006, 10:49 AM

Search Tags


/mathhelpforum @mathhelpforum