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

1. Nov 15, 2009

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!

2. Nov 15, 2009

Cryphonus

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?

3. Nov 15, 2009

sprizz

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

4. Nov 15, 2009

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

5. Nov 15, 2009

D H

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