A space probe of mass m p =2000 kg carries fuel of mass m f =300 kg. initially,

Question

A space probe of mass mp=2000 kg carries fuel of mass mf=300 kg. initially, the (probe + Fuel) is approaching a planet at V0 = 1000 m/s as measured from a "fixed" control station on Earth. It is desired to slow the probe to 950 m/s (relative to Earth) in order to get it into orbit around the planet. This is accomplished by firing fuel through a "forward-facing" rocket on the probe. The rocket fires burnt fuel forward at 800 m/s relative to the probe.

Is it possible to accomplish this operation with the amount of available fuel? If so, how many kilograms of fuel will need to be burnt?

Explanation / Answer

suppose it expels mass of fuel m

then
conservation of momentum

(2000 + 300)*1000 = (2000 + 300-m)*950 + m*1800

m=135.3 kg

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