You are on Mars and would like to send a probe into space so that it does not fall back to the surface. What minimum launch speed do you need? (The mass of Mars is 6.42x10^23 kg and the radius of Mars is 3.40x10^6 m)

Question

You are on Mars and would like to send a probe into space so that it does not fall back to the surface. What minimum launch speed do you need? (The mass of Mars is 6.42x10^23 kg and the radius of Mars is 3.40x10^6 m)
km/s

Please someone also help me on this.I really don't know how to do this.Thank you.

bobpursley · Answer

PE at surface= GMm/r PE mars= GMmars*m/rm PE earth= GMe*m/re so on mars, you have to overcome the PE at the surface, or 1/2 m v^2=GMmars*m/rmars velocity= sqrt(2G*MassMars/radiusMars)