Calculating Orbital Speed: Jupiter & Earth Orbit Time

[ubiquitous]

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.

 

[LowlyPion]

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?

 

[nlightner]

I would recommend using the equation for orbital speed:

V = √(GM/r)

Where:
V = orbital speed (m/s)
G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
M = mass of the central body (Jupiter in this case, in kg)
r = distance from the center of the central body to the object (9.5 x 10^6 km + radius of Jupiter, converted to meters)

For the first question, plug in the values and solve for V. Remember to convert the distance to meters before plugging it into the equation.

For the second question, the value of Cs is the standard gravitational parameter for Jupiter, which is a constant value used in orbital mechanics calculations. To find the time for one orbit, you can use the following equation:

T = 2πr/V

Where:
T = time for one orbit (s)
r = average radius of orbit for Jupiter (7.78 x 10^11 m)
V = orbital speed (calculated from the first question)

Again, remember to convert the radius to meters before plugging it into the equation. This will give you the time in seconds, so you can convert it to years by dividing by the number of seconds in a year (3.154 x 10^7 s).

I hope this helps and good luck with your calculations! Remember to always double-check your units and conversions to ensure accuracy.