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? I got this
400 pounds...
2. The radius of the Earth were 1.5 times its present value?
3. The radius of the Earth were .5 its present value?

Answer 1

1.) Without knowing the speed of the spacecraft, you can't answer either question.

2.) g = Gm1m2/r^2. Since the mass of Mary is negligible, and the Gravitational constant is constant:
Δg = Δm/Δr^2
W = We * Δg (We = Weight on earth)

1. Δg = 4/1 (because r does not change), so Mary weighs 400 lbs.
2. Δg = 1/(1.5^2) (because m does not change) = 1/2.25. W = 100 / 2.25 = 44.44 lbs.
3.) Δg = 1/(.5^2) (because m does not change) = 1/.25. W = 100 / .25 = 400 lbs.