- #1

Honore

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__QUESTION:__A space station orbits the sun at the same distance as the Earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed (m/s) does the probe need to escape the solar system?

__MY UNDERSTANDING AND SOLUTION:__The escape speed v from a sphere of radius R and mass M is given by the energy-conservation equation as follows: (from "Schaum's 3000 Solved Problems in Physics" book, page 101)

**(1/2)*m*v^2 = G*M*m / R**where;

M: mass of the sun (=1.98*10^30 kg)

m: mass of the small probe

R: Radius of the sun (=6.95*10^8 m)

G: Universal Gravitation Constant [=6.67*10^(-11) Nm^2/kg^2]

From the equation typed in bold above;

v = sqrt(2*G*M / R) and using the numerical values v is found about

616479 m/s .

What do you think?

Thanks.