Centripetal acceleration of a satellite orbiting Earth

In summary, a satellite orbiting the Earth in a stable orbit has a centripetal acceleration of 1/4 g.
  • #1
ride4life
33
0

Homework Statement


A satellite is orbiting the Earth in a stable orbit of which the radius is twice that of the Earth. Find the ratio of the satellites cepripetal acceleration to g on the Earth's surface.


Homework Equations


centripetal acceleration = (v^2)/r or (4rpi^2)/T^2


The Attempt at a Solution


Well the only thing i can figure is the rafius of the satellite which is 12.8x10^6
Otherwise I have no idea where to start :(
 
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  • #2
Hi ride4life! :smile:

(try using the X2 tag just above the Reply box :wink:)

As usual, it's good ol' Newtons' second law that's needed, this time together with another of Newton's laws! :-p

What does that give you? :smile:
 
  • #3


Ummm...
Fc=Fg
mac=Fg
mac=mg
ac=g
?
 
Last edited:
  • #4
ride4life said:
F=mg
g=GM/r2

ok … now combine that with your original g = v2/r :smile:
 
  • #5


v2=GM/r
v2=(6.67x10-11x6x1024)/6.4x106
v=7907.67m/s
 
  • #6


ahhh...

ac=GM/r2
ac=(6.67x10-11x6x1024)/(2x6.4x106)2
ac=2.44
 
  • #7


Remember to always include the units or else the answer makes no physical sense.
 
  • #8
Sorry, not following this …

you're making it very complicated :redface:

The question only asks for the centripetal acceleration (as a multiple of g on the Earths' surface) …

you have centripetal acceleration = GM/r2, so … ? :smile:
 
  • #9


centripetal acceleration = 2.44
ratio compared to Earth's g which is 9.8 is 2.44/9.8 which is about 1:4
 
  • #10


It is only "about" 1:4 because of the over-complicated way you did that. That was tiny-tim's point. It isn't necessary to find the actual accelerations.

[tex]a= \frac{GM}{r^2}[/tex]
If r= 2R (R is the radius of the earth) then
[tex]a= \frac{GM}{(2R)^2}= \frac{GM}{4r^2}= \frac{1}{4}\frac{GM}{r^2}= \frac{1}{4}g[/tex].

The centripetal acceleration of a satellite at radius twice the radius of the Earth is exactly 1/4 g.
 
  • #11


ahhh...
i see what you mean, way less complicated than my way :biggrin:
 

Related to Centripetal acceleration of a satellite orbiting Earth

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and is responsible for keeping the object in its circular orbit.

2. How is centripetal acceleration related to the orbit of a satellite around Earth?

In the context of satellite orbiting Earth, centripetal acceleration is the force that keeps the satellite in its circular orbit around the planet. It is provided by the gravitational pull of Earth and is directly proportional to the square of the satellite's distance from the center of the planet.

3. How does the mass of a satellite affect its centripetal acceleration?

The mass of a satellite does not affect its centripetal acceleration. This is because according to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since the gravitational force acting on the satellite is dependent on the mass of the planet and the distance between the satellite and the planet, the mass of the satellite itself does not have an impact on its centripetal acceleration.

4. What factors affect the centripetal acceleration of a satellite in orbit?

The centripetal acceleration of a satellite is affected by the mass of the planet it is orbiting, the distance between the satellite and the planet, and the speed of the satellite. These factors determine the strength of the gravitational force acting on the satellite, which in turn determines the centripetal acceleration needed to keep the satellite in its orbit.

5. Can the centripetal acceleration of a satellite change during its orbit?

Yes, the centripetal acceleration of a satellite can change during its orbit. This is because the distance between the satellite and the planet changes as the satellite moves along its elliptical orbit. As the distance changes, the gravitational force acting on the satellite also changes, resulting in a change in its centripetal acceleration.

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