Calculating Solar System Reach of Pioneer Craft Without Assist

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Homework Help Overview

The discussion revolves around calculating the potential reach of the Pioneer spacecraft in the solar system without the gravitational assist from Jupiter. The original poster is confused about the appropriate parameters to use in their calculations, particularly regarding the mass of the Sun and the distance from Earth to the Sun.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply a formula involving gravitational potential energy but questions whether to use the mass of the Sun instead of the mass of the Earth. They also express confusion about the initial conditions and the distance from the Earth to the Sun.

Discussion Status

Participants are exploring the implications of using different masses in their calculations. Some guidance has been provided regarding the use of the Sun's mass and the cancellation of the spacecraft's mass in the equations. However, there is still uncertainty regarding the initial distance from the Earth to the Sun.

Contextual Notes

The original poster notes that they do not have the value for the Earth's distance from the Sun, which is necessary for their calculations. Another participant provides this value, indicating that it can be used in the context of the problem.

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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...
 
Last edited:
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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?
 
Last edited:
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)?
 
Last edited:
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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