What is the Orbital Speed of a Satellite at 7000 km Altitude?

AI Thread Summary
To determine the orbital speed of a satellite at an altitude of 7000 km, the gravitational force must be balanced with the centrifugal force. The mass of the Earth is 5.98 x 10^24 kg, and the radius of the Earth is 6.38 x 10^6 m. The gravitational force can be calculated using the formula Fg = GM/R^2. After finding Fg, the orbital speed can be derived from the equation mv^2/r. This approach effectively combines gravitational and centripetal forces to solve for the satellite's speed.
JohnnyB212
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Homework Statement



A satellite is in circular orbit above the Earth at an altitude of 7000 km. What is the orbital speed of the satellite?

Homework Equations



Well, knowing that the mass of Earth of 5.98 X 10^24 kg

And the radius of Earth is 6.38 x 10^6 m
What equation do I start with here? The "speed" portion is what's getting me. :frown:
 
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Orbit means that the gravitational force inward and the centrifugal force outward are balanced. The centrifugal force depends on the angular speed and this with the radius will give you the speed.
 
First you need to find the Fg and that would be using the GM/R^2 formula once u have Fg you can get v using mv^2/r
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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