If the radius of the Earth is R and a satellite is in a circular orbit at a heig

Practice Questions

If the radius of the Earth is R and a satellite is in a circular orbit at a height h above the Earth's surface, what is the expression for the orbital speed v of the satellite?

v = sqrt(GM/(R+h))
v = sqrt(GM/R)
v = sqrt(GM/(R-h))
v = sqrt(GM/(R^2 + h^2))

Questions & Step-by-Step Solutions

If the radius of the Earth is R and a satellite is in a circular orbit at a height h above the Earth's surface, what is the expression for the orbital speed v of the satellite?

Step 1: Understand that the radius of the Earth is R.
Step 2: Recognize that the satellite is at a height h above the Earth's surface.
Step 3: Realize that the total distance from the center of the Earth to the satellite is R + h.
Step 4: Recall that the gravitational force provides the necessary centripetal force for the satellite's circular orbit.
Step 5: Use the formula for gravitational force: F = GMm/(R+h)^2, where M is the mass of the Earth and m is the mass of the satellite.
Step 6: Set the gravitational force equal to the centripetal force: F = mv^2/(R+h).
Step 7: Cancel the mass of the satellite (m) from both sides of the equation.
Step 8: Rearrange the equation to solve for v: v^2 = GM/(R+h).
Step 9: Take the square root of both sides to find the orbital speed: v = sqrt(GM/(R+h)).

Gravitational Forces – Understanding how gravitational forces act on objects in orbit and the relationship between mass, distance, and gravitational acceleration.
Orbital Mechanics – Knowledge of the principles governing the motion of satellites and the derivation of formulas related to orbital speed.
Circular Motion – Application of circular motion principles to derive the speed of an object in a circular path.

If the radius of the Earth is R and a satellite is in a circular orbit at a heig

Practice Questions

Questions & Step-by-Step Solutions

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