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Chapter 13: Q. 18 (page 353)

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 does the probe need to escape the solar system?

Short Answer

Expert verified

The minimum speed that the probe needs to escape the solar system is42.06km/s.

Step by step solution

01

Given information 

The space station orbits the sun at the same distance as the earth i.e. the sun's radius.

02

Calculation

The expression for the minimum speed for the probe to escape from the solar system is given by according to the law of conservation of energy is : v=2G脳MR.

Where 'v' is the escape velocity.

'G' is the universal gravitational constant.

'M' is the mass of the sun.

'R' is the distance between sun and earth orbitlocalid="1648486344262" =1.5脳1011m.

03

Continuation of calculation

Now, all the known values are substituted to find 'v' :

v=2G脳MRv=2(6.67脳10-11Nm2/kg2)(1.989脳1030kg)(1.5脳1011m)v=42058m/sv=42.06km/s.

04

Final answer

The probe needs to have a minimum speed of 42.06km/s to escape from the solar system.

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