Physics satellite velocity and period

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Homework Help Overview

The discussion revolves around calculating the tangential velocity of a satellite in a circular orbit 300 km above the Earth's surface, utilizing gravitational equations and understanding the relationship between altitude and orbital radius.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore how to incorporate the altitude of 300 km into the calculation of the orbital radius and subsequently the velocity. Questions arise regarding the correct formulation of the radius and the importance of unit consistency.

Discussion Status

Participants are actively engaging in clarifying the calculations needed for the orbital radius and velocity. Some guidance has been provided regarding the need to convert units and ensure the radius used in calculations reflects the total distance from the Earth's center.

Contextual Notes

There is an ongoing discussion about the correct interpretation of the radius in the gravitational formula, with emphasis on the need to add the Earth's radius to the altitude of the satellite. Participants also highlight the importance of unit conversion in their calculations.

astru025
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Homework Statement



a. What is the tangential velocity of a satellite in a circular orbit 300km above the surface of the Earth?

Homework Equations


Velocity of a satellite= v^2= G (Me/r)


The Attempt at a Solution


V^2= 6.67E-11 (5.98E24/6.37E6)
I calculated this and my answer proved incorrect. How do I incorporate the "300 km above Earth's surface" into this equation?.
 
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astru025 said:
How do I incorporate the "300 km above Earth's surface" into this equation?.
Use that to calculate the radius of the orbit, which will be "r".
 
I use 300km to calculate the radius of the orbit. What is the equation for the radius?
 
astru025 said:
I use 300km to calculate the radius of the orbit. What is the equation for the radius?
In your calculation, you set r = radius of the earth. But that's not correct; r should be the radius of the orbit, which is bigger than the radius of the Earth (by the given amount).

First calculate the radius of the orbit, then use it in your formula to find the speed.
 
Okay thank you. Is there a special equation to find the radius of the orbit?
 
astru025 said:
Is there a special equation to find the radius of the orbit?
Just add the altitude of the orbit, which was given, to the radius of the earth.
 
Okay so now I have : v^2= G (6.67E-11) x ((Me (5.98E24) / (r + 300 km. (6670 km))
Is this correct? So I got 244540.39.
 
That answer was incorrect. What am I doing wrong?
 
Did you check your units? Always check your units.
 
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  • #10
astru025 said:
Okay so now I have : v^2= G (6.67E-11) x ((Me (5.98E24) / (r + 300 km. (6670 km))
Is this correct? So I got 244540.39.
I don't understand how you got that answer. Did you make sure to put the radius in meters, not km?
 
  • #11
This must be it. You are off by a factor of about √1000. The radius should be in meters.
 
  • #12
Okay I finally came up with 1768897.96 m/s
 
  • #13
Okay now I came up with 7733.046. This must be correct. Miscalculation in my previous try.
 
  • #14
This proved correct! Thanks so much. Always need to check my units :)
 

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