Calculating Solar System Reach of Pioneer Craft Without Assist

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The discussion centers on calculating how far the Pioneer spacecraft would travel in the solar system without a gravitational assist from Jupiter. The initial speed of the spacecraft relative to the Sun was 38 km/s, and a formula involving gravitational potential energy is proposed to determine the final distance from the Sun. Participants suggest using the mass of the Sun in the calculations and provide the Earth's distance from the Sun as approximately 1.496 x 10^11 meters. It is clarified that the spacecraft's mass cancels out in the equations, simplifying the problem. The conversation highlights confusion around the calculations but ultimately leads to a clearer understanding of the required parameters.
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another problem bout satellites...

to exit the solar system, the Pioneer spacecraft used a gravitational assist from jupiter, which increased its kinetic energy at the expense of Jupiter's kinetic energy. If the spacecraft did not have assist, how far out in the solar system would it travel? when it left Earth's vicinity, the spacecraft speed's relative to the sun, was 38km/s.
r=2GM/v^2
=2(6.673x10^-11N m^2/kg^2)(5.98x10^24kg)/(38000m/s)^2
r=552694.4598m

shoudld i use the mass of the sun coz the answer in my book is 7.9x10^11m
i don't know wat to do, I am so confused...
 
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six789 said:
another problem bout satellites...

to exit the solar system, the Pioneer spacecraft used a gravitational assist from jupiter, which increased its kinetic energy at the expense of Jupiter's kinetic energy. If the spacecraft did not have assist, how far out in the solar system would it travel? when it left Earth's vicinity, the spacecraft speed's relative to the sun, was 38km/s.
r=2GM/v^2
=2(6.673x10^-11N m^2/kg^2)(5.98x10^24kg)/(38000m/s)^2
r=552694.4598m

shoudld i use the mass of the sun coz the answer in my book is 7.9x10^11m
i don't know wat to do, I am so confused...
TWO (2) changes are required (assuming spacecraft of mass "m" applies no additional engine power & isn't significantly influenced by other astronomical entities):
a) Use Sun's mass for "M".
b) Use change in Potential Energy from {Earth's distance from Sun "Dearth"} to the {Unknown final distance from Sun "Dfinal"}:
(1/2)*m*(vinitial)2 = -G*m*M*{(1/Dfinal) - (1/Dearth)} = G*m*M*{(1/Dearth) - (1/Dfinal)}
Solve for "Dfinal".


~~
 
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xanthym, i don't know the {Earth's distance from sun "Dearth"}. can u give me the value for that?
 
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six789 said:
xanthym, i don't know the {Earth's distance from sun "Dearth"}. can u give me the value for that?
If your textbook doesn't provide {Earth's distance from Sun "Dearth"}, you can use the following:
Dearth = 1.496e(11) meters


~~
 
pioneer

u know that the Pioneer has no given mass?? so what will i put to the m in 1/2 mv^2 nad GmM(1/r - 1/r)?
 
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six789 said:
u know that the Pioneer has no given mass??
Spacecraft's mass "m" cancels out from both sides of equation.


~~
 
ohh yeahhhh... i forgot
 
thanks so much for the help, xanthym! hope u can help me again... heheh =)
 

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