Astronomy Basics: Solving Problems with Earth & Mars

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The discussion revolves around solving two problems related to orbital mechanics and gravitational attraction. For the first problem, the user is trying to calculate Mars' orbital period using Kepler's third law but is confused about unit conversions and the resulting high values. The second problem involves finding the mass of a second sphere based on the gravitational force between two spheres, but the user is uncertain about how to apply the gravitational force formula correctly. Participants suggest checking unit conversions and applying Kepler's laws properly for the first problem, while also clarifying the gravitational force equation for the second. Overall, the user seeks guidance on both problems to arrive at reasonable answers.
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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seang said:
I'm not totally sure how to do the first part, but I'd check into Kepler's laws.

In particular the third one. :smile:
 
well i have done the third law and i get a really high answer which i am pretty sure can't be right.
 
vintagechic1251 said:
well i have done the third law and i get a really high answer which i am pretty sure can't be right.

Could you show us what you did?
 

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