How do you find the mass of the Sun using data about planet periods and radii?

[sprizz]

How do find the mass of the Sun using the following data:
Planet r ... T
Mercury 57.9... 0.241
Venus 108... 0.615
Earth 150... 1
Mars 228... 1.88
Jupiter 778 ... 11.9
Saturn 1,430... 29.5
Uranus 2,870... 84
Neptune 4,500... 165
Pluto 5,900... 248

The problem says we should graph r^3 against T^2.

I assume we're meant to use:

$$M = \frac{4 \pi^2}{GT^2} r^3$$

I've tried to graph them in all sorts of different ways but I can't find out how to find the mass of the Sun using the information. Please help!

 

[Cryphonus]

How do find the mass of the Sun using the following data:
Planet r ... T
Mercury 57.9... 0.241
Venus 108... 0.615
Earth 150... 1
Mars 228... 1.88
Jupiter 778 ... 11.9
Saturn 1,430... 29.5
Uranus 2,870... 84
Neptune 4,500... 165
Pluto 5,900... 248

The problem says we should graph r^3 against T^2.

I assume we're meant to use:



$$M = \frac{4 \pi^2}{GT^2} r^3$$

I've tried to graph them in all sorts of different ways but I can't find out how to find the mass of the Sun using the information. Please help!

Dear Sprizz;

The formula that you write above is one of kepler's laws. you have the periods and raidus's provided to you and the "M" value on your formula is the mass of the sun...So i think its all about calculations after that?

 

[sprizz]

Right, but how would one use graphing T^2 and r^3 to arrive at such an answer?

 

[Cryphonus]

Well all i can think is that the T² r³ graph is going to give you a constant.It will be the value of 4Pi²/G.Msun and it should be same for all planets.If you know this value you can calculate the mass of the sun but its not really different from what i told you before, there is only a graph included... hope it helped

 

[D H]

Right, but how would one use graphing T^2 and r^3 to arrive at such an answer?

Try plotting T^2 on the horizontal axis and r^3 on the vertical axis. What do you get?