# Homework Help: Period of a planet.

1. Mar 18, 2005

### 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.

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2. Mar 18, 2005

### 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 $$\sqrt(GM)$$.

3. Mar 18, 2005

### witze

Kepler's Third Law!!

4. Mar 18, 2005

### SpaceTiger

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

5. Mar 18, 2005

### 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.

6. Mar 18, 2005

### SpaceTiger

Staff Emeritus
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.

7. Mar 18, 2005

### witze

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