1. Not finding help here? Sign up for a free 30min 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!

Questions About Satellites Orbiting Earth

  1. Jun 28, 2011 #1
    1. The problem statement, all variables and given/known data
    I have a satellite with a mass of 250 kg, which I'm launching from Earth. This neglects air resistance/rotation of the planet etc.
    • a. How much energy is needed to put the satellite in orbit at an altitude of 4.0 x 106 m?
    • b. What would be the period of the satellite at that altitude?
    • c. How much additional energy would be needed to put the satellite into a geosynchronous orbit?

    2. Relevant equations
    Period=2pir/T
    PE=G(mM/r)
    KE=(1/2)(m)(v^2)

    3. The attempt at a solution
    This is my first day doing orbital problems, so I'm really having trouble getting started! For a, I thought maybe I should calculate velocity then the kinetic energy using 1/2mv^2? And then add it to the potential energy of the satellite when it's orbiting, using PE=mgh?For b, I know a formula to find the period. For c, I've never seen a problem like that, but I assume I would put 24 hours into the period equation and start from there? Thank you in advance!
     
    Last edited: Jun 28, 2011
  2. jcsd
  3. Jun 28, 2011 #2

    rock.freak667

    User Avatar
    Homework Helper

    For part a, you just need to get the PE from the surface of the earth to that altitude.
     
  4. Jun 28, 2011 #3
    Okay! I did:
    PEi=G([(250 kg)(5.97 x 10^24 kg)]/[6378100 m])
    PEf=G([(250 kg)(5.97 x 10^24 kg)]/[6378100 m + 4.0 x 10^6 m])
    The difference between the two was 6007709504 J.
    (5.97 x 10^24 kg is what I used as the mass of the earth, and 6378100 m is what I used as the radius of the earth).
    Does that look okay?
     
  5. Jun 28, 2011 #4

    rock.freak667

    User Avatar
    Homework Helper

    I think that should be correct.

    For the second part, use the fact that gravitation force of attraction between the Earth and the satellite = centripetal force on the satellite to get the period.
     
  6. Jun 28, 2011 #5

    gneill

    User Avatar

    Staff: Mentor

    Question for pondering: Do you want to take into account the fact that the satellite, when it's sitting on the launching pad, already has a speed around the Earth's center due to the rotation of the Earth?
     
  7. Jun 28, 2011 #6
    Nope! My teacher said we're not considering it.
     
  8. Jun 28, 2011 #7

    gneill

    User Avatar

    Staff: Mentor

    Okay, you've worked out the energy that you have to supply in order to climb to the appropriate height above the Earth, now you need to impart an orbital velocity (KE) in order that it can stay there. What's the required velocity for a circular orbit at a given orbital radius r?
     
  9. Jun 28, 2011 #8
    I'm not sure how to show the gravitational force between earth and the satellite--should I use mg?

    Also, one of my friends told me just to calculate the PE of the satellite above earth as PE=G([250 kg)(5.97 x 10^24)]/(4.0 x 10^6]), which gives a total of 24887437.5 J, which is a different answer. How can I tell which is right?
     
  10. Jun 28, 2011 #9
    mg = m(v^2/r), but should I use regular gravity?
     
  11. Jun 28, 2011 #10

    gneill

    User Avatar

    Staff: Mentor

    Your friend is confused about the distinction between altitude (above Earth's surface) and orbital radius (around Earth's center).
     
  12. Jun 28, 2011 #11

    gneill

    User Avatar

    Staff: Mentor

    'mg' only applies near the Earth's surface. Use the full Newtonian gravitation formula for the force (and the PE).
     
  13. Jun 28, 2011 #12
    GmM/d^2 = m(v^2/r)?
     
  14. Jun 28, 2011 #13
  15. Jun 28, 2011 #14

    rock.freak667

    User Avatar
    Homework Helper

    In this case d is the same as r, so you can get v which will help you to get ω.

    Your first equation in the relevant equations should be

    T = 2π/ω
     
  16. Jun 28, 2011 #15
    What is ω? I don't think I've learned it yet. Is it a symbol?
     
  17. Jun 28, 2011 #16

    rock.freak667

    User Avatar
    Homework Helper

    Angular velocity which is found in circular motion. It has a simple relation to v and r.
     
  18. Jun 28, 2011 #17
    Oh--we haven't done that in my class! Is there a way to avoid it?
     
  19. Jun 28, 2011 #18

    rock.freak667

    User Avatar
    Homework Helper

    Well usually when you learn circular motion and centripetal force (mv2/r), you would learn about angular velocity and how it relates to velocity and radius.

    Are you given the formula for kepler's third law where T2∝r3 ?
     
  20. Jun 28, 2011 #19
    Yes, I do have that!
     
  21. Jun 28, 2011 #20

    rock.freak667

    User Avatar
    Homework Helper

    ah in that case you can rewrite T2∝r3 as T2=Kr3, your notes should have what is needed to calculate the constant K.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Questions About Satellites Orbiting Earth
  1. Satellite Orbiting Earth (Replies: 13)

Loading...