Sorry for reposting this but I'm still confused with the last part...

You have been sent in a small spacecraft to rendezvous with a space station that is in a low circular Earth orbit, say, with a radius of 6,720 km, approximately that of the orbit of the International Space Station. Due to mishandling of units by a technician, you find yourself in the same orbit as the station but exactly halfway around the orbit from it! A smaller elliptical orbit fail unpleasantly. Keeping in mind that the life-support capabilities of your small spacecraft are limited and so time is of the essence, can you perform a similar maneuver that will enable you rendezvous with the station? Find the radius and period of the transfer orbit you should use.
The perihelion is
The aphelion is
The period is

Physics - drwls, Saturday, May 7, 2011 at 12:15am
Apply an impulse to the spaceship in the direction of motion to put it into a larger elliptical orbit. The location that the impulse is applied will remain the perihelion location. Apply enough impulse to make the period 50% longer. After the small spacecraft has made one more orbit, the space station will have made 1.5 orbits and be in the right place.

perihelion: 6720 km
semimajor axis a can be otained from a Kepler relation:
(a/6720)^2 = (1.5)^3
a = 6720*(1.5)^1.5 = 12,345 km

Period = 1.5 x original period (about 135 minutes). You can calculate it from original orbit radius

Thanks. So will the aphelion be the perihelion + 2a = 31,410 km??

In order to calculate the period, won't I need the velocity?

Physics - drwls, Saturday, May 7, 2011 at 1:32am
No. See my answer elsewhere

Physics - Catherine, Saturday, May 7, 2011 at 2:17am
I must be doing something wrong because I typed the answers for a second time and they are wrong, I have only one attempt left, can you please check what I did wrong?

For the period what I did was
P = sqrt(R^3(4pi^2)/GM)
P = sqrt ((6720^3(4pi^2)/(6.674E-11(5.9742E24)))
P = 0.1733 s

0.1733 x 1.5= 0.2600
and for the anphelion I got
aphelion = 2a - perihelion
= 2(12,345)-6720
= 17,970 km

Both answers are wrong...

Physics - bobpursley, Saturday, May 7, 2011 at 5:46am
Your period calculation. How can you think that .17 seconds can possibly be right for orbiting the Earth? Your radius in the numbers is in km, you need it in meters. I get about 311 seconds for period, work it out.

Physics - drwls, Saturday, May 7, 2011 at 7:19am
There is still something wrong with the period calculation. It should be over 90 minutes.

Physics - Catherine, Saturday, May 7, 2011 at 2:59pm
Thanks, I now get 5481 seconds for the period, then I have to multiply that by 1.5 right? I get 8222 s

When you say substitute a for R, you meant for the equation of the aphelion?

Physics - drwls, Saturday, May 7, 2011 at 4:33pm
a is the semimajor axis. Substitute it for R in the equation that relates period to R.

Remember that many orbits with periods longer than 3/2 the circular-orbit period (such 5/4 or 7/6) will also work.. they just take longer to rendezvous.

I'm sorry, I don't understand, you mean this equation: P = 2pi sqrt[R^3/(GM)]
won't "a" be 12,345 km?

So is the period 8222 s?

I still don't get why the ansser for the aphelion is wrong...

  1. 👍 0
  2. 👎 0
  3. 👁 50
  1. 8222 s is one possible period that will work. There are others, as i have tried to explain.

    For any period P you choose, you can use

    P = sqrt(a^3(4pi^2)/GM)
    to get the semimajor axis, a.

    The perihelion remains the same after the maneuver. The new aphelion distance is
    2a - (perihelion)

    If these numbers don't work for you, I can't explain why.

    Those are my last words on this subject

    1. 👍 0
    2. 👎 0
    posted by drwls
  2. Just wanted to thank you for answering all my questions even though I was clearly lost during most of this process... I finally got it... Thanks =D

    1. 👍 0
    2. 👎 0
  3. Concept Simulation 3.2 at reviews the concepts that are important in this problem. A
    golfer imparts a speed of 30.3 m/s to a ball, and it travels the maximum possible distance
    before landing on the green. The tee and the green are at the same elevation. (a) How
    much time does the ball spend in the air? (b) What is the longest “hole in one” that the
    golfer can make, if the ball does not roll when it hits the green?

    1. 👍 0
    2. 👎 0
    posted by EDGAR

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra 1

    just reposting :):) i still don't really get it. "Tweedledum says: the sum of your weight and twice mine is 361 lbs. Tweedledee says: contrariwise, the sum of your weight and twice mine is 362 lbs if both are right how much do

    asked by Melanii on February 17, 2009
  2. research

    What year did the Holocaust begin?when did it end and how? I've already answered that twice in the last day or so on this board. Please look back on all of your posts and their answers. If you don't want to read the answers you

    asked by Brooke on May 15, 2007
  3. chemistry

    Can Anyone Help Me With This Solubility Problem? An aqueous solution of 1.90 M AgNO3 is slowly added from a buret to an aqueous solution of 0.0100 M Cl- and 0.250 M I-. b) When the second ion begins to precipitate, what is the

    asked by anonymous on April 21, 2010
  4. Calculus

    (a) Find dy/dx given that x^2+y^2-4x+7y=15. (b) Under what conditions on x and/or y is the tangent line to this curve horizontal? Vertical? For part A, I simplifid it to -(2x+4/2y+7) For part B,I am confused on what to do?

    asked by George on November 7, 2008
  5. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to

    asked by ~christina~ on September 16, 2007
  6. Algebra

    I have one more question I need to ask about algebra, this one is a perform the indicated operation question. 4x 5x ----- - ---- x^2-9 x^2+4x-+3 I am really confused on the -+3 part, I don't know if my teacher made a typo or what,

    asked by Jeff on March 18, 2008
  7. social studies

    I need help checking my question. Explain why the Confederacy spared Washington d.c from being destroyed? my answer. Washington was surrounded by strong fortifications and was filled to the brim with Union troops and because they

    asked by dude on February 19, 2015
  8. Math

    Hi. The question I'm having problems with: Write the body of an iterative function to compute n!, where n! = n(n-1)(n-2)...1. Then, analyze this function where the work unit is the multiplication operation. I think I have the

    asked by Iah on May 3, 2007
  9. physics

    I;m sorry, but I was stuck on the second part of this problem. Can you please help me? An automobile engine slows down from 4500 rpm to 1500 rpm in 2.5 seconds. a) calculate angular accceleration b)calculate total number of

    asked by Morgan on March 23, 2010
  10. physics

    I;m sorry, but I was stuck on the second part of this problem. Can you please help me? An automobile engine slows down from 4500 rpm to 1500 rpm in 2.5 seconds. a) calculate angular accceleration b)calculate total number of

    asked by Morgan on March 23, 2010
  11. Calculus AB

    So the problem is "For x>0, d(lnx)/dx = 1/x and lne=1. A) find the tangent line approximation for ln 3 B) calculate the %error in approximation in part A. My teacher said the answer for part A is that 1/e, and I'm pretty confused.

    asked by Annie on January 30, 2017

More Similar Questions