The distance of the satellite form the earth is:
9,608,000 m (Option C) in Standard form, this is written as 9.6 x 10[tex]^{6}[/tex].
What is an Orbiting Satellite?
An Orbiting Satellite is a satellite that goes around the earth in an elliptical path known as an orbit.
To calculate the distance of the satellite from the earth we must equalize the force of Gravity to Centripetal Force given that these are the two forces that are at play here.
Step 1:
Equation that equalizes Gravity to Centripetality is:
G = mM/r² = m(v²/r)
Note that G = 6.67 x 10[tex]^{-11}[/tex] (This is a gravitational constant.)
m is the Mass of the Satellite
M is Mass of the Earth
r is the distance of the satellite from the center of the earth
v is the satellites tangential velocity
Step 2 - Rearrange the formula and substitute the numbers above to get r
r = G (m/v²) = (6.67 x 10[tex]^{-11}[/tex]) (6 x10[tex]^{24}[/tex]/5000²) =
= 1.6 x 10[tex]^{7}[/tex]m
Recall that form our postulation above, this is the satellites distance form the center of the earth.
To get it's distance form the earth's surface, we must know remove the value of the radius of the earth from the calculation. Where radius of the earth is given a r'
Hence,
r' = r - R = 1.6 x 10[tex]^{7}[/tex]m - 6.4 x 10[tex]^{6}[/tex]m
= 9.6 x [tex]10^{6}[/tex]m or 9,608,000 m
Learn more about orbiting satellites at:
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