Planetary Motion HW: Orbit Radius & Speed Around Jupiter

In summary, the explorer is planning a mission to place a satellite into a circular orbit around Jupiter with a radius of R. In order to be synchronized with Jupiter's rotation, the required orbital radius is calculated to be 1.59374x108 meters. The orbital speed would need to be 28207.7 m/s to maintain this orbital period. If the orbital speed is slower than needed, the orbit would be smaller than desired, and if it is faster, the orbit would be larger and possibly more elliptical.
  • #1
k-rod AP 2010
36
0

Homework Statement


An explorer plans a mission to place a satellite into a circular orbit around Jupiter, the radius of the planned orbit would be R.

a)The explorer wants the satellite to be sychronized w/ Jupiter's rotation. Determine the required orbital radius in meters.
b) What must the orbital speed of this satellite be in order to maintain this orbital period?



Homework Equations


RJ=7.14x107m
MJ=1.9x1027kg
Jupter's rotational period=3.55x104s
[tex]G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}[/tex]

The Attempt at a Solution


a) T=√(4π2R3/GMJ)
3.55x104s=√(4π2R3/GMJ)
R=1.59374x108 m

b)v=√(GMJ/R)
v=√(GMJ/1.59374x108 m)
v=28207.7 m/s

arm I following the correct procedure on these problems? i am trying to get a handle on this planetary motion stuff and i am not sure if i have yet.
 
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  • #2
Your method is correct.
 
  • #3
ok, that's what i thought thanks for the help. and another question pertaining to this hw,...

if the orbital speed were mistakingly made slower than needed the orbit would be smaller than desired, and if it were faster than needed the orbit would be larger and more elliptical than wanted right?
 
  • #4
k-rod AP 2010 said:
ok, that's what i thought thanks for the help. and another question pertaining to this hw,...

if the orbital speed were mistakingly made slower than needed the orbit would be smaller than desired, and if it were faster than needed the orbit would be larger and more elliptical than wanted right?

Not too sure how elliptical it would be in real life, but with the assumption of circular motion

Fc=mv2/r, if 'v' were smaller, the 'r' would need to be smaller to maintain the same Fc, and if 'v' were larger, 'r' would be larger as well. So yes you are correct, but once again, I am not too sure how elliptical the motions would become.
 
  • #5
ok that's what i was thinking, thanks again for all your help with this problem
 

1. What is the formula for calculating orbit radius and speed around Jupiter?

The formula for calculating orbit radius is r = a(1-e^2)/(1+e*cos(theta)), where a is the semi-major axis, e is the eccentricity, and theta is the true anomaly. The formula for calculating orbital speed is v = sqrt(GM(2/r - 1/a)), where G is the gravitational constant, M is the mass of Jupiter, r is the orbit radius, and a is the semi-major axis.

2. How do the orbit radius and speed of a satellite around Jupiter change over time?

The orbit radius and speed of a satellite around Jupiter remain constant unless acted upon by an external force. However, due to the gravitational pull of other bodies in the solar system, the orbit radius and speed may experience slight variations over time.

3. What factors affect the orbit radius and speed around Jupiter?

The orbit radius and speed around Jupiter are primarily affected by the mass and gravitational pull of Jupiter, as well as the mass and distance of any nearby bodies. Other factors that can affect the orbit include the eccentricity of the orbit and the presence of any external forces.

4. How does the orbit radius and speed of a satellite around Jupiter compare to that of a satellite around Earth?

The orbit radius and speed around Jupiter are typically larger and faster than that of a satellite around Earth. This is due to the larger size and mass of Jupiter, which results in a stronger gravitational pull and a longer orbital period.

5. Can the orbit radius and speed around Jupiter be changed or adjusted?

Yes, the orbit radius and speed around Jupiter can be changed or adjusted by altering the velocity of the satellite. This can be achieved through the use of propulsion systems or by utilizing gravitational assists from other bodies in the solar system.

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