Orbital Velocity Homework: Find Velocity of Geostationary Satellite

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Homework Help Overview

The discussion revolves around finding the orbital velocity of a geostationary satellite, which is positioned at a distance of 35,900 km above Earth's surface. Participants are exploring the necessary equations and concepts related to orbital mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the circumference of the orbit and converting units, but express uncertainty about the correctness of their answer. There is mention of the gravitational force acting as the centripetal force, and questions arise regarding the need for the satellite's mass and the use of angular versus linear velocity. Some participants also inquire about centripetal acceleration and its calculation based on available information.

Discussion Status

The discussion is active, with participants sharing their thoughts on the relationships between gravitational and centripetal forces. Guidance has been offered regarding the cancellation of the satellite's mass in the equations and the focus on linear velocity. Multiple interpretations of the problem are being explored, particularly concerning the use of centripetal acceleration and the relevant equations.

Contextual Notes

Participants note the absence of the satellite's mass as a constraint, and there is an ongoing discussion about the necessary expressions for centripetal and gravitational forces. The problem setup and assumptions are being questioned, particularly regarding the parameters needed for calculations.

zeion
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Homework Statement



Basically says that a geostationary satellite requires a distance of 35 900 km above Earth's surface. I need to find its orbital velocity.

Homework Equations





The Attempt at a Solution



I find the circumference of the orbit = 225566.3525km then change units to m/s but the answer is wrong?
 
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The gravitational force between the satellite and the Earth is proving the centripetal force of the satellite. From the equation for centripetal force you have velocity.
 
But I'm not given the mass of the satellite
 
zeion said:
But I'm not given the mass of the satellite

When you equate the two, the mass of the satellite cancels out.
 
Do I need to use the angular velocity?
 
zeion said:
Do I need to use the angular velocity?

No, I believe that they are asking you for the linear velocity which is the 'v' in the expression for centripetal force.
 
So I need to use centripetal acceleration?
 
zeion said:
So I need to use centripetal acceleration?

Essentially yes.
 
How do I calculate that? I only have the radius and the period.
 
  • #10
zeion said:
How do I calculate that? I only have the radius and the period.

Do you know the expressions for centripetal force and gravitational force?
 
  • #11
F = (mv^2) / r ?
 
  • #12
zeion said:
F = (mv^2) / r ?

then put that equal to the expression for gravitational force and find 'v'.
 
  • #13
Is that F = ma?
 
  • #14
zeion said:
Is that F = ma?

No you should know that F=GMm/r2 where 'r' is the distance between the Earth and the satellite.
 

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