Question

derive an expression for orbital velocity of planet in terms of gravitational constant, radius of the orbit and mass of the sun​

Answer 1

Answer:

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Answer 2

Orbital velocity in terms of orbital radius, the mass of earth, and gravitational constant.

Step-by-step explanation:

Let:

G = gravitational constant

M = mass of earth

R = radius of Earth

m = mass of a satellite

h = distance from the surface of Earth at which the satellite os revolving

so, r = R + h (radius of the orbit)

Now,

for a satellite to revolve a centripetal force of $\frac{MV^{2} }{r}$ is acted. ...........(1)

gravitational force is also acted $\frac{GMm}{r^{2} }$  ...........(2)

On equating the forces in (1) and (2)

$\frac{MV^{2} }{r} = \frac{GMm}{r^{2} }$

$V = \sqrt{\frac{GM}{r} } = \sqrt{\frac{GM}{R + h} }$   (Orbital Velocity)