Answer :
The velocity of the satellite in a stable circular orbit around the Earth at a height of [tex]3700 km[/tex] is approximately [tex]7026 m/s[/tex].
Why will be stable circular orbit about the Earth at a height of 3700 km?
To calculate the velocity of a satellite in a stable circular orbit around the Earth at a given height, we can use the formula:
[tex]v = sqrt(GM/R)[/tex]
where v is the velocity of the satellite, G is the gravitational constant [tex](6.674 x 10^-11 Nm^2/kg^2)[/tex], M is the mass of the Earth [tex](5.972 x 10^24 kg)[/tex], and R is the radius of the orbit.
First, we need to convert the height of the satellite above the Earth's surface to the radius of the orbit. We know that the radius of the Earth is approximately [tex]6,371 km[/tex], so the radius of the orbit is:
[tex]R = height of satellite above Earth's surface + radius of Earth\\[/tex]
[tex]R = 3700 km + 6371 km[/tex]
[tex]R = 10071 km[/tex]
Now we can plug in the values and calculate the velocity:
[tex]v = sqrt(GM/R)[/tex]
[tex]v = sqrt((6.674 x 10^-11 Nm^2/kg^2)(5.972 x 10^24 kg)/(1.0071 x 10^7 m))[/tex]
[tex]v = 7026 m/s[/tex]
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Final answer:
To calculate the velocity of a satellite in a stable circular orbit, we can use the formula: velocity = √((G * M) / (r + h)). Using the given height of 3700 km, we can calculate the velocity of the satellite using this formula.
Explanation:
To calculate the velocity of a satellite in a stable circular orbit about the Earth at a given height, we can use the formula:
velocity = √((G * M) / (r + h))
Where G is the gravitational constant, M is the mass of the Earth, r is the radius of the Earth, h is the height of the satellite above the Earth's surface. Plugging in the values for G, M, r, and h, we can calculate the velocity of the satellite.
Using the given height of 3700 km, we can substitute this value into the formula and calculate the velocity of the satellite.
