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

In summary, the problem asks for the mass of the Sun, which can be found using Kepler's law. The formula given asks for the period and radius of each planet, which are given to you. After plotting these values, one should calculate the mass of the Sun using 4 pi r3.
  • #1
sprizz
2
0
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:

[tex]
M = \frac{4 \pi^2}{GT^2} r^3
[/tex]

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!
 
Physics news on Phys.org
  • #2
sprizz said:
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:



[tex]
M = \frac{4 \pi^2}{GT^2} r^3
[/tex]

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?
 
  • #3
Right, but how would one use graphing T^2 and r^3 to arrive at such an answer?
 
  • #4
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
sprizz said:
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?
 

1. How do you determine the mass of the Sun using data about planet periods and radii?

The mass of the Sun can be calculated using the third law of planetary motion, which states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis (distance from the Sun). By knowing the period and semi-major axis of a planet, we can use this formula to calculate the mass of the Sun.

2. What data is needed to calculate the mass of the Sun using planetary orbits?

To calculate the mass of the Sun using planetary orbits, we need to know the orbital period and semi-major axis of at least one planet. These can be obtained from observational data or through calculations based on the planet's distance from the Sun and its orbital speed.

3. Can the mass of the Sun be accurately determined using data from just one planet?

No, the mass of the Sun cannot be accurately determined using data from just one planet. This is because the third law of planetary motion only gives a proportional relationship between the mass of the Sun and the orbital period and semi-major axis of a planet. Therefore, data from multiple planets is needed to accurately calculate the mass of the Sun.

4. How does the mass of the Sun affect the orbits of planets?

The mass of the Sun is a major factor in determining the orbits of planets. The greater the mass of the Sun, the stronger its gravitational pull, which affects the speed and distance of a planet's orbit. Planets with smaller distances from the Sun and shorter orbital periods have a greater mass for the Sun.

5. What other factors can affect the accuracy of calculating the mass of the Sun using planetary data?

Aside from the number of planets and their orbital data used in the calculation, the accuracy of determining the mass of the Sun can also be affected by factors such as the accuracy of the measurements, the presence of other objects in the solar system, and the effects of general relativity. These factors should be taken into account when using planetary data to calculate the mass of the Sun.

Similar threads

How to Linearize Data for Solar System Motion Analysis?
    • Introductory Physics Homework Help
Replies
3
Views
2K
How Can You Calculate Saturn's Mass Using a Telescope and Stopwatch?
    • Introductory Physics Homework Help
Replies
9
Views
2K
Orbits of the planets and centripetal acceleration
    • Advanced Physics Homework Help
Replies
1
Views
8K

Hot Threads

Recent Insights

Back
Top