Speed of satellite in circular orbit

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Homework Help Overview

The problem involves calculating the speed of a satellite in a circular orbit around the Earth, given the mass of the Earth and the orbital period of the satellite.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of formulas for orbital speed and period, with some attempting to derive the radius from the given period. There are questions about the accuracy of the calculated radius and speed, with some participants suggesting re-evaluating calculations.

Discussion Status

The discussion has seen multiple attempts to calculate the radius and speed, with some participants expressing uncertainty about their results. There is a recognition of potential calculation errors, and one participant seeks verification of their final speed calculation.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can use or the methods they can apply. There is an ongoing exploration of assumptions related to the formulas used.

thatgirlyouknow
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Homework Statement



A satellite is in a circular orbit about the Earth (M = 5.98 x 1024 kg). The period of the satellite is 9.93 x 104 s. What is the speed at which the satellite travels?

Homework Equations



v=(2*pi*r)/T

v=sqrt((GMe)/r)

The Attempt at a Solution



sqrt[((6.67x10^-11)*(5.98x10^24))/r) = 2*pi*r / T
T = 2piR^3/2 / (sqrt[GMe])
r = 8.414 x 10^15
v = 2*pi*r / t
v = 5.324 x 10^11 m/s
 
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thatgirlyouknow said:

Homework Statement



A satellite is in a circular orbit about the Earth (M = 5.98 x 1024 kg). The period of the satellite is 9.93 x 104 s. What is the speed at which the satellite travels?

Homework Equations



v=(2*pi*r)/T

v=sqrt((GMe)/r)

The Attempt at a Solution



sqrt[((6.67x10^-11)*(5.98x10^24))/r) = 2*pi*r / T
T = 2piR^3/2 / (sqrt[GMe])
r = 8.414 x 10^15

your formula looks right but I think r is wrong... check your calculations
 
Ok after reworking I got that r = 46357704 m. So:

v = sqrt[(GMe)/r]
v = sqrt[(6.67x10^-11*5.98x10^24)/(46357704)]
v = 3594.51 m/s

But this still isn't right. Are my calculations wrong at some point?
 
Ok I worked it again and got v = 2933.27 m/s. (Hooray human error). Can anyone verify that as correct?
 
thatgirlyouknow said:
Ok I worked it again and got v = 2933.27 m/s. (Hooray human error). Can anyone verify that as correct?

yes, looks right to me.
 

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