Calculating Solar System Reach of Pioneer Craft Without Assist

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In summary, the conversation discusses the use of a gravitational assist from Jupiter to increase the kinetic energy of the Pioneer spacecraft, allowing it to exit the solar system. Without this assist, the spacecraft would have traveled to a distance of approximately 552694.4598 meters from the sun. However, using the mass of the sun and the change in potential energy, the final distance can be calculated to be approximately 7.9x10^11 meters. The conversation also mentions the cancellation of the spacecraft's mass in the equation.
  • #1
six789
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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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  • #2
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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  • #3
xanthym, i don't know the {Earth's distance from sun "Dearth"}. can u give me the value for that?
 
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  • #4
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


~~
 
  • #5
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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  • #6
six789 said:
u know that the Pioneer has no given mass??
Spacecraft's mass "m" cancels out from both sides of equation.


~~
 
  • #7
ohh yeahhhh... i forgot
 
  • #8
thanks so much for the help, xanthym! hope u can help me again... heheh =)
 

1. How do you calculate the solar system reach of Pioneer craft without assistance?

The solar system reach of Pioneer craft without assistance can be calculated using the escape velocity formula, which takes into account the mass of the spacecraft, the mass of the Sun, and the distance between them. This formula gives the minimum speed needed for a spacecraft to escape the gravitational pull of the Sun and continue on its journey through the solar system.

2. What is the escape velocity of the Pioneer spacecraft?

The escape velocity of the Pioneer spacecraft is approximately 17 km/s. This means that in order to escape the Sun's gravitational pull, the spacecraft needs to reach a speed of at least 17 km/s.

3. Does the Pioneer spacecraft have any other means of propulsion?

Yes, the Pioneer spacecraft is equipped with thrusters that can provide additional propulsion. However, these thrusters are primarily used for course corrections and adjustments rather than for long-distance travel.

4. How far can the Pioneer spacecraft travel without assistance?

Based on its current trajectory and speed, the Pioneer spacecraft has the potential to travel beyond the edge of our solar system and enter interstellar space. However, it is estimated that it will take approximately 80,000 years for it to reach this point.

5. What is the main limitation of calculating the solar system reach of Pioneer craft without assistance?

The main limitation is the unpredictable nature of space. The spacecraft may encounter unexpected obstacles or gravitational forces that could alter its trajectory and limit its reach. Additionally, the spacecraft's equipment and technology may degrade over time, further limiting its capabilities.

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