Astronomy Basics: Solving Problems with Earth & Mars

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vintagechic1251
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yes, i am defintely not a genius at this stuff...

i am having some problems figuring these two problems out:

Earth is 1.5x10^11 m from the Sun and has a period of 365.2 days. Mars is an average of 2.28x10^11 km from the sun. what is the orbital period of Mars in Earth years?

i am not exactly sure on what to do. should i convert m to km or the other way around? and i am not exactly sure on what equation to use either. i have used keplers third law to come out with an equation of the period of Mars is equal to the square root of the Earth's period squared times the radius of Mars over the radius of Earth cubed... i am getting really high answers like 5612 days and such. am i missing something?

i am also having problems with:

two spheres are 1.02 km apart. one of the spheres has a mass of 57.0 kg, and the force of attraction between the spheres is 1.79x10^-14 N. find the mass of the other sphere.

i'm not exactly sure on how to do that one because of the "force of attraction" i am not sure where i plug that value into. i have an equation of force times radius squared over gravitational force (6.67x10^-11) times the mass of the first sphere. and the answer i get when i do this is slightly unreasonable.

your help is greatly appreciated :smile:
 
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I'm not totally sure how to do the first part, but I'd check into Kepler's laws. You should take a look at your units too; perhaps you mean miles, not meters for Earth's radius of rotation.

For the second part, remember that the gravitational interaction between tow objects is found by:

F = (G*m1*m2)/r^2

G is a constant: 6.674E-11
 
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well i have done the third law and i get a really high answer which i am pretty sure can't be right.