satellites again...

six789

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 dont know wat to do, im so confused...

xanthym

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 "D_earth"} to the {Unknown final distance from Sun "D_final"}:
(1/2)*m*(v_initial)² = -G*m*M*{(1/D_final) - (1/D_earth)} = G*m*M*{(1/D_earth) - (1/D_final)}
Solve for "D_final".


~~

six789

xanthym, i dont know the {Earth's distance from sun "Dearth"}. can u give me the value for that?

xanthym

If your textbook doesn't provide {Earth's distance from Sun "D_earth"}, you can use the following:
D_earth = 1.496e(11) meters


~~

six789

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)?

xanthym

Spacecraft's mass "m" cancels out from both sides of equation.


~~

six789

ohh yeahhhh... i forgot

six789

thanks so much for the help, xanthym!! hope u can help me again... heheh =)