Calculate Orbital Radius of Planet X

[bobo1455]

Homework Statement

Calculate orbital radius of planet X using the given variables of its star: T=500 K, radius R=0.1 x Sun's radius, mass M=0.5 x Sun's mass and also its receives the same flux as the Earth receives from the Sun. I forgot to mention also that the orbit is circular, so the orbital radius=distance between planet X and its star.

Homework Equations

Probably Newton's version of kepler's third planetary motion equation, but not really sure.

The Attempt at a Solution

I have tried using various forms of keplers' third planetary motion equation, but I don't have the period of orbit, like in hours, so I have more than one missing variable. Besides that, I've tried looking for an equation to yield the orbital radius using the variables I'm given but I've got nothing so far. The other thing I thought of is that maybe I can use equations for a binary pair of stars to calculate Planet X's orbital radius, but I didn't know how to proceed with it.

 

[SteamKing]

Homework Statement

Calculate orbital radius of planet X using the given variables of its star: T=500 K, radius R=0.1 x Sun's radius, mass M=0.5 x Sun's mass and also its receives the same flux as the Earth receives from the Sun. I forgot to mention also that the orbit is circular, so the orbital radius=distance between planet X and its star.

Homework Equations

Probably Newton's version of kepler's third planetary motion equation, but not really sure.

The Attempt at a Solution

I have tried using various forms of keplers' third planetary motion equation, but I don't have the period of orbit, like in hours, so I have more than one missing variable. Besides that, I've tried looking for an equation to yield the orbital radius using the variables I'm given but I've got nothing so far. The other thing I thought of is that maybe I can use equations for a binary pair of stars to calculate Planet X's orbital radius, but I didn't know how to proceed with it.

If you don't have the period or any other orbital data, then you have to find something else to use to calculate the orbital radius of planet X.

The problem statement describes the star in detail. You are given the size of the star, its temperature, its mass, and the fact that the planet receives the same stellar flux as the Earth receives from the sun.

Forget Kepler for the time being and concentrate on the last clue.

https://en.wikipedia.org/wiki/Luminosity#Stellar_luminosity

 

[bobo1455]

So maybe I can somehow use the formula F = L/(4*pi*(d^2))? I read the link you gave me on wikipedia. I'll try using L ≈ 4πR^2σT^4 to calculate the star's luminosity and then substitute in for L in the other equation I have and re-arrange and solve for d. Not really sure what to do after that...

 

[SteamKing]

So maybe I can somehow use the formula F = L/(4*pi*(d^2))? I read the link you gave me on wikipedia. I'll try using L ≈ 4πR^2σT^4 to calculate the star's luminosity and then substitute in for L in the other equation I have and re-arrange and solve for d. Not really sure what to do after that...

Remember, you can also use the ratios between the luminosity of the star in the OP and what happens with the sun and the Earth in the solar system. There should be a relationship between the size of the star and its temperature which you can ratio against what the sun puts out, its temperature,and its size.

 

[bobo1455]

I'm having a hard time understanding your last post. I've read it like 15 times now and still have no clue what you mean. Are you saying to to make an equation like this:

F1 / F2 = L1 / L2 ?

 

[SteamKing]

I'm having a hard time understanding your last post. I've read it like 15 times now and still have no clue what you mean. Are you saying to to make an equation like this:

F1 / F2 = L1 / L2 ?

No, I'm saying look at the ratios given in the article on stellar luminosity.

There is a formula which relates the luminosity of an arbitrary star with the luminosity of the sun:

​

That's the approach which I think may help.

 

[JoAstro]

Hi, bobo1455.

I have the same kind of problem only with different values. I was wondering if you found your answer.
I am struggling a lot to get an answer since I don't know where to start. -- I was told the flux of the Sun is the key, but I can't see any relation to what I need to do to be able to start.

Thanks

 

[bobo1455]

You can use the formula that SteamKing posted assuming you have all of the variables except for the variable you're trying to figure out.

The main thing to remember is that orbital radius is the same as the distance between the object and it's star if the orbit of the object is circular (meaning eccentricity = 0), so try solving an equation for the distance between the two objects.