1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distance of the Earth and Sun

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate the relative change in the distance of the Earth from the Sun, if the mass of the Sun is 15% lower than today weight of the Sun. Suppose that the Earth moves and will move along a circular path and will maintain its angular momentum.


    2. Relevant equations
    Equality of gravitational and centrifugal forces.


    3. The attempt at a solution
    For mass of the Sun today:
    Valid for Earth: The centrifugal force = gravitational force
    m_e*(v)^2/r=κ*m_e*m_s/(r)^2
    (v)^2=κ*m_s/r


    For mass of the Sun when is 15% lower than today weight of the Sun:
    Valid for Earth: The centrifugal force = gravitational force
    Mass and velocity of the Earth does not change because it does not change angular momentum.
    m_e*(v)^2/r_1=κ*0,85m_s*m_e*/(r_1)^2
    (v)^2=κ*0,85m_s/r_1

    Equal squares of velocities:
    κ*m_s/r=κ*0,85m_s/r_1
    1/r=0,85/r_1

    When is r=1 AU, then r_1=0,85AU

    Why? I think it's stupid. Why the Earth is closer to the Sun, when the Sun is lighter? I think must be the Earth from the Sun farther, because the gravitational effects diminish. Why my ideas don't coincide with the results? How would you counted it?

    Thanks very much.
     
  2. jcsd
  3. Feb 25, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The angular momentum is mvr. The product of the radius and speed is unchanged.


    ehild
     
  4. Feb 25, 2013 #3
    Sorry, but I do not understand you too much. Please, could you explain to me what to fix to make it right in great detail?
     
  5. Feb 25, 2013 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The speed of Earth (v) changes. Conservation of angular momentum means that mer v is conserved.

    ehild
     
  6. Feb 26, 2013 #5
    Well, I get it, thank you very much :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Distance of the Earth and Sun
  1. Sun and the Earth (Replies: 1)

Loading...