Period of Red Planet: Find Average Yearly Period

[dalitwil]

In the figure the blue planet has a period of 1 year and an average distance from the sun of 1.73 x 1011 meters. If the average distance from the sun for the red planet is 1.39 x 1011 meters, what is its period to the nearest hundredth of a year?

So I thought maybe they through in the information on the blue planet to confuse me, so disregarding that information, I used the formula:

T=(2pi/square root of GM)*r^3/2
where G=6.67e-11 and M is the mass of the sun=2.0e30kg

Unfortunately, this isn't correct, and I don't see where I am supposed to incorporate the information about the blue planet with the red planet.

 

[clive]

Maybe you are not supposed to use the values for M and G in this problem. Just write the expressions of T for the two planets and eliminate $$\sqrt(GM)$$.

 

[witze]

Kepler's Third Law!

 

[SpaceTiger]

In the figure the blue planet has a period of 1 year and an average distance from the sun of 1.73 x 1011 meters. If the average distance from the sun for the red planet is 1.39 x 1011 meters, what is its period to the nearest hundredth of a year?

Did you learn Kepler's Law? All you need is a proportionality.

 

[dalitwil]

Right, the period T is proportional to r^3/2 (Kepler's 3rd law), but I am still unsure how to relate the two planets using this concept.

 

[SpaceTiger]

Right, the period T is proportional to r^3/2 (Kepler's 3rd law), but I am still unsure how to relate the two planets using this concept.

If

$$x^m \propto y^n$$

then, if you have two systems that fit the proportionality:

$$\frac{x_1^m}{x_2^m}=\frac{y_1^n}{y_2^n}$$

This applies to all values of m and n.

Proportionality just implies that there is some constant out front. If you have a test case with which to determine that constant, that's all you need.

 

[witze]

T^2/a^3=const for all planets orbiting the same massive object.