What is the Mass of the Planet in Scientific Notation?

[free_spirit]

Hi all :)

Hope the day has been good to you...i am stuck on a question for my uni assignment, and have been stuck on this one for about 3 days to no avail...i don't even know where to start. I'm not too sure whether i need a certain equation for the question or if i have to come up with one using the information in the question...
If anyone could please help me through it would be greatly appreciated as I've only got 4 days left...if not thanks for looking anyways :)


There once was a planet - quite far
In orbit around a star
The star’s mass was ms
The planet’s mass you assess
Using the orbital radii, r


You can assume the radius of the planet’s and the star’s circular orbits around the
centre of mass of the system are r_p = 1.5 × 10⁸ km and r_s = 1.0 × 10⁶ km, respectively, with
m_s = 2.0 × 10³⁰ kg.

Calculate the mass of the planet, m_p, showing all your workings and giving your answer in scientific notation to the appropriate number of significant figures.


Any help would be amazing as I'm at my wits end !
Many Thanks,

Ax

 

[free_spirit]

So far all the info i have is that;

a) the star is 1 million miles from the centre of mass
b) the planet is 150 million miles from the centre of mass; and
c) both bodies are in circular orbits to the centre...

so I'm not too sure how to use this data to calculate the answer...

Ax

 

[PeterO]

So far all the info i have is that;

a) the star is 1 million miles from the centre of mass
b) the planet is 150 million miles from the centre of mass; and
c) both bodies are in circular orbits to the centre...

so I'm not too sure how to use this data to calculate the answer...

Ax

I think I would treat it as a simple centre of Mass problem. With the planet 150 times forther from the centre of mass I think it should simple be 1/150 th of the mass of the Sun.

 

[free_spirit]

ok thanks very much PeterO :)

i have done a calculation but am not too sure whether this is correct at all...

m_p = r_p x r_s
m_s

so,

m_p = 1.5 x 10⁸km x 1.0 x 10⁶km
2.0 x 10³⁰kg

m_p = 150 000 000 000 000
2.0 x 10³⁰kg

m_p = 0.000 000 000 000 000 075 ??

ok, so i am also now thinking that this is incorrect...gah !

thanks for the help though, much appreciated :)

 

[gneill]

So far all the info i have is that;

a) the star is 1 million miles from the centre of mass
b) the planet is 150 million miles from the centre of mass; and
c) both bodies are in circular orbits to the centre...

so I'm not too sure how to use this data to calculate the answer...

Ax

How did you end up with miles as units when the problem appears to use kilometers?

 

[free_spirit]

oops !

my bad, sorry bout that i did mean kilometres...sorry been at this for a while now and my brain is kinda mushy...thanks for pointing that out