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!

Determine altitude

  1. Oct 1, 2009 #1
    1. The problem statement, all variables and given/known data

    The satellite S travels around the earth in a circular path with a constant speed of 20 Mm/h. If the acceleration is 2.5m/s2, determine the altitude h. Assume the earth's diameter to be 12 713 km.

    i5akx3.png

    2. Relevant equations

    [tex]a_{n}= \frac{v^{2}}{\rho}[/tex]

    3. The attempt at a solution

    I thought that [tex]a_{t}= 0[/tex] because speed is constant and [tex]a_{n}= 20 Mm/h[/tex] and I just solved the above equation for [tex]\rho[/tex] but that came out to a negative number so that's not right.
     
  2. jcsd
  3. Oct 1, 2009 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Why are you using the tangential speed as the acceleration? The acceleration is, as you have stated, [itex]a = v^2/r[/itex]. But there is another expression for a as well, since the acceleration is provided by .....? Write the equation for that acceleration. With those two equations you should be able to solve for the two unknowns, a and r.

    AM
     
  4. Oct 1, 2009 #3
    Ops that was a typo. I meant [tex]a_{n}= 2.5 m/s^{2}[/tex]
     
  5. Oct 1, 2009 #4

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Ok. I misread the question too. You are given the acceleration. What units must v have in your equation [itex]a_n = v^2/r[/itex]?

    AM
     
  6. Oct 1, 2009 #5
    v should be m/s I think. Which I calculated 20 Mm/h = 5555.556 m/s
     
  7. Oct 2, 2009 #6

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    So what is r? How is r related to h?

    AM
     
  8. Oct 2, 2009 #7
    I am assuming r would be to the center of the earth and h is r - the earths radius.
     
  9. Oct 2, 2009 #8
    Ok I think I got this:

    [tex]v = 20 Mm/h = 5555.6 m/s[/tex]

    [tex]a_{n} = 2.5 m/s^{2}[/tex]

    [tex]a_{n}= \frac{v^{2}}{\rho}[/tex]

    [tex]\rho= \frac{v^{2}}{a_{n}}[/tex]

    [tex]\rho= \frac{5555.6}{2.5} = 12345679.01 m[/tex]


    [tex]h = \rho - earth's radius = 12345679.01 - 6356500 = 5989179.01 = 5989.18 km[/tex]
     
  10. Oct 2, 2009 #9

    rock.freak667

    User Avatar
    Homework Helper

    that looks better now, I think you were getting a negative number because you were subtracting the diameter instead of the radius.
     
  11. Oct 2, 2009 #10
    Ya that's what I was doing.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook