Calculating Orbital Speed: Jupiter & Earth Orbit Time

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To calculate orbital speed, the gravitational force and centripetal force must be balanced. The equation for orbital speed is derived from the gravitational force formula, using the mass of the planet and the radius of the orbit. For Jupiter, the average radius of orbit is 7.78 x 10^11 m, and the gravitational constant (Cs) is 3.355 x 10^18 m^3/s^2. To find the time for one orbit, apply Kepler's third law, which relates the orbital period to the semi-major axis of the orbit. Understanding these principles will allow for the correct calculations of both orbital speed and orbital period.
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ok just a couple orbital questions I forget the equation that needs to be used and do not have my textbook with me so if anyone knows the equation for finding orbital speed that would be great!

1. calculate the speed of a satellite in orbit 9.5 x10^3 km above jupiter.
radius of Jupiter = 7.18 x 10^7 m
Mass of Jupiter = 1.90 x 10^27 kg

2. The average radius of orbit for Jupiter is 7.78 x 10^11m. usuing Cs = 3.355 x 10^18 m^3/s^2, calculate the number of Earth years it will take for Jupiter to complete one orbit.

So what does it mean by Cs and how do you find the time for one orbit? I have trouble getting the problems started if I'm given a hint i can usually find the answers on my own so anything will help.
 
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ubiquitous said:
ok just a couple orbital questions I forget the equation that needs to be used and do not have my textbook with me so if anyone knows the equation for finding orbital speed that would be great!

1. calculate the speed of a satellite in orbit 9.5 x10^3 km above jupiter.
radius of Jupiter = 7.18 x 10^7 m
Mass of Jupiter = 1.90 x 10^27 kg

2. The average radius of orbit for Jupiter is 7.78 x 10^11m. usuing Cs = 3.355 x 10^18 m^3/s^2, calculate the number of Earth years it will take for Jupiter to complete one orbit.

So what does it mean by Cs and how do you find the time for one orbit? I have trouble getting the problems started if I'm given a hint i can usually find the answers on my own so anything will help.

Welcome to PF.

You can always figure out what you want.

You know the Gravitational Force.

And it will balance with the centripetal force won't it?
 
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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