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Book Free DemoFormula of orbital velocity:
The orbital velocity is calculated using the formula,
Where,
\(G\) is the Gravitational constant (\(6.673 \times 10^{–11}\) \(Nm^2kg^{-2}\)),
\(M\) is the mass of the Earth (\(5.972 \times 10^{24}\) \(kg\)),
\(R\) is the radius of the Earth (\(6371\ km\)),
\(h\) is the height of the satellite from the Earth's surface
Example:
Calculate the orbital velocity of a satellite orbiting at an altitude of \(500\ km\) above Earth?
\(G\) \(=\) \(6.673 \times 10^{–11}\) \(Nm^2kg^{-2}\)
\(M\) \(=\) \(5.972 \times 10^{24}\) \(kg\)
\(R\) \(=\) \(6731000\ m\)
\(h\) \(=\) \(500000\ m\)
The formula is given as
On substituting the given values, we get
Thus, the orbital velocity of a satellite is \(7.613\ kms^{-1}\).
Time period of a satellite:
The time taken by a satellite to complete one revolution around the Earth is called the time period (\(T\)).
On substituting the values of \(v\), we get
Example:
Find the orbital period of the satellite at an orbital height of \(500\ km\).
\(h\) \(=\) \(500\ km\)
\(R\) \(=\) \(6731\ km\)
\(v\) \(=\) \(7.613 kms{-1}\)
The formula is given as
On substituting the given values, we get
Thus, the orbital period of the satellite is \(95\ minutes\).