Help on physics/astronomy problem...?

Question

You want to send a spacecraft from Earth to Mars [P(Mars)=1.88 yrs; a(Mars) = 1.52 AU]

1. What is the period of the spacecraft's orbit?
b. How long will it take the spacecraft to get to Mars?
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Mary weighs 100 pounds. Compared to what she weighs now, how much would she weigh if:

1. The mass of the Earth were 4 times its present value?
2. The radius of the Earth were 1.5 times its present value?
3. The radius of the Earth were .5 its present value?

Tell me how to do one.. and I'll the the rest for this problem..

Thanks.

Nvm, I got the answers for the second problem..

Answer 1

OK, there are actually many answers to the first question, depending on how powerful your rocket is. But let's assume you are calculating a minimum energy Hohmann transfer orbit. By Kepler's 3rd law, T2=D3, which is the square of the orbital period is proportional to the cube of the diameter of the orbit. By Kepler's 2nd law we know that all of the orbits that share the same major axis have the same period. So all you have to do is calculate the period of an orbit whose major axis is 1.0+1.52, i.e.2.52, compared to 2.0(Earth) or 3.04(Mars). Don't forget to divide by two for a one way trip, unless you just want to "fly by" Mars and return to Earth again.
The 2nd problem just uses the inverse square law, assuming as Newton did that all of the mass of the Earth is concentrated in the center. The answers would be a)400, b)100/2.25, c)400

Answer 2

ok well for question 1. the period will depend on the the speed of the spacecraft. are you supposed to use the orbital period of earth and mars for reference? or an average? and for part b, how long really depends on how fast you want to get there. you can take years to get there if you want or only a few months. All depends on how much fuel you want to burn.

So basically you need more info to answer the question, or you have to make some assumptions.

but here is how you go about it, AFTER you make some assumptions
http://www.go.ednet.ns.ca/~larry/orbits/orbitrnf.html

the rest is left as an exrecise for the reader.