Question #f0549

1 Answer
Andrew I.
Jan 13, 2018

#7427.18ms^(-1)#

Explanation:

The centripetal force is given by:

#F=(m_2v^2)/r#

and the force of gravity by:

#F=(Gm_1m_2)/r^2#

As the centripetal force is provided solely by the force of gravity in orbital mechanics then set these equal to each other:

#(Gm_1m_2)/r^2=(m_2v^2)/r#

Rearrange for #v#:

#->(Gm_1)/r=v^2->v=sqrt((Gm_1)/r)#

The values are:

#G=6.67times10^(-11)Nkg^-2m^2# (The universal gravitational constant)
#r=(850+6371)km=7221times10^(3)m# (Radius of the earth plus the height of the satellite)
#m_1=5.972times10^24kg#

Sub into formula for #v#.

#v=sqrt(((6.67times10^(-11))(5.972times10^(24)))/(7221times10^3))=7427.18ms^(-1)#

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