SOLUTION: A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet. Then NASA boosted the satellite to an altitude one mile hig

Question 114345: A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?
(C=2pir)
>>>>>>>>>>>>PLEASE I NEED YOUR HELP.....THANKS IN ADVANCE
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A NASA satellite makes a circular orbit around a planet of unknown diamter at an altitude of one mile above the planet.
Then NASA boosted the satellite to an altitude one mile higher(an altitude of two miles above planet.) In the second orbit, the satellite travels how many miles farther than it travelled on the first orbit?
(C=2pir)
----------------
Lower orbit distance = 2(pi)(r+1) where r is the radius of the unknown planet.
-------------------
Upper orbit distance = 2(pi)(r+2)
-----------------
Difference EQUATION:
2(pi)(r+2)-2(pi)(r+1) = 2(pi)[(r+2)-(r+1)] = 2(pi) miles
==============
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You don't know the diameter of the planet, so let's call that miles. The first orbit is one mile above the planet, so we know that the diameter of the orbit is . We had to add 2 because 1 mile of altitude adds 1 mile to the radius, and the diameter is twice that. Now, if we move out to a point 2 miles above the surface, the diameter of the new orbit is .
We know that the distance travelled in the first orbit is the circumference of the circle with diameter , or , and the distance travelled in the second orbit is .

Now we can subtract: => => => miles. Not too far, really, just a little over six and a quarter miles.

Hope this helps,
John
RELATED QUESTIONS
A satellite makes a circular orbit around a planet of unknown diameter at an altitude of... (answered by stanbon)
A satellite has a circular orbit around a planet with a radius of 4350 mi. The satellite... (answered by ikleyn)
A satellite has a circular orbit around a planet with a radius of 4580 mi. The satellite... (answered by Alan3354)
A centripetal force of 150 N acts on a 1,100-kg satellite moving with a speed of 5,100... (answered by ikleyn)
An orbit of a satellite around a planet is an ellipse, with the planet at one focus of... (answered by ikleyn)
Assume that the planet�s orbit is circular at a radius 500 million kilometers from its... (answered by Alan3354)
Planet A's satellite has an elliptical orbit described by X`2/(4963)`2+... (answered by KMST,ikleyn)
(b) As shown in the figure (2), three satellites are equally spaced in equatorial... (answered by greenestamps)
The orbit of a planet around a star is described by the equation... (answered by MathLover1)