Calculate the mass of a star and a planet that orbits it

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I have problem with an A2 physics question:

A planet is orbiting a star at an average distance of 10^9 km. The period of its orbit is 500 Earth days. The gravitational constant is 6.67x10^-11 Nm^2kg^2.
a) Calculation the mass of the star.
b)Explain why you cannot determine the mass of the planet from this information.

I think I should use this equation:
T^2=4π^2r^3/GM
not sure how should I calculate T from 500!
r is 10^9km I suppose!

for part b I'm not sure what should I say.
I appreciate any help with this question. Many thanks

Last edited:

gneill
Mentor
I have problem with an A2 physics question:

A planet is orbiting a star at an average distance of 10^9 km. The period of its orbit is 500 Earth days. The gravitational constant is 6.67x10^-11.
Kind of a poorly posed question. The average distance can vary greatly compared to the semi-major axis depending upon the eccentricity of the orbit. I presume you'll have to assume a circular orbit (very low eccentricity). The gravitational constant should come with units. What are they?
I think I should use this equation:
T^2=4π^2r^3/GM
Looks reasonable.
not sure how should I calculate T from 500!
What are the units used in your value of G? You need to use consistent units in all your values and variables.
r is 10^9km I suppose!
Suppose so. But be sure to match the "length" unit used in your gravitational constant definition.
for part b I'm not sure what should I say.
You'll have to ponder what assumptions were made in the derivation of the period formula you've used.

Many thanks. I have just added the units of G.

Homework Statement

A planet is orbiting a star at an average distance of 10^9 km. The period of its orbit is 500 Earth days. The gravitational constant is 6.67x10^-11 Nm^2kg^2.
a) Calculation the mass of the star.
b)Explain why you cannot determine the mass of the planet from this information.

Homework Equations

T^2=4π^2r^3/GM
1 earth day is 24 hours which is 24x3600 s
T= 500x24x3600 s

The Attempt at a Solution

for part a)
I think I should rearrange it for M which I know how to do it.
1 earth day is 24 hours which is 24x3600 s
T= 500x24x3600 s
is T correct?
and r=10^9x1000 m#
for part b)
this part has 3 marks and I think part of the answer is :
because this formula is independent from the mass of the planet. I am not sure if this is correct .Plus I don't know what else to say

Buzz Bloom
Gold Member
I think part of the answer is :
because this formula is independent from the mass of the planet. I am not sure if this is correct .
Hi shk:

You are correct. However, I would phrase it a bit differently.
The variables T, r, and M are independent of the planet mass.

Regards,
Buzz

thanks. But would that be enough to get the 3 marks for part b?

Buzz Bloom
Gold Member
But would that be enough to get the 3 marks for part b?
Hi shk:

If I were you teacher it would be, but it is impossible for me to predict exactly what your teacher wants. You might want to take another look at my previous post since I added to it after you replied to it.

Regards,
Buzz

Thanks Buzz
Thanks a lot

wolf1728
Gold Member
Maybe I'm joining the discussion a bit late here, but perhaps I can offer some help.
The equation you need is:
mass = (4 * PI² * r³) / (G * t²)
where mass ('m') is in kilograms, radius ('r') is in meters) time ('t') is in seconds and G = 6.674 * 10^-11 m³/kg*s²
time ('t') should be in seconds so 500 days * 24hours*60minutes*60seconds = 43,200,000 seconds
radius ('r') should be in meters 10^9 km = 10^12 meters and you will have to calculate:
mass = (39.4784 * (10^12 meters)³ / (6.674 * 10^-11 m³/kg*s² * (43,200,000 seconds)²
The mass will be in kilograms
I hope this helps

shk
Maybe I'm joining the discussion a bit late here, but perhaps I can offer some help.
The equation you need is:
mass = (4 * PI² * r³) / (G * t²)
where mass ('m') is in kilograms, radius ('r') is in meters) time ('t') is in seconds and G = 6.674 * 10^-11 m³/kg*s²
time ('t') should be in seconds so 500 days * 24hours*60minutes*60seconds = 43,200,000 seconds
radius ('r') should be in meters 10^9 km = 10^12 meters and you will have to calculate:
mass = (39.4784 * (10^12 meters)³ / (6.674 * 10^-11 m³/kg*s² * (43,200,000 seconds)²
The mass will be in kilograms
I hope this helps
Dear Wolf1728
It wasn't still late and it did help .
Many thanks

wolf1728
Gold Member
Just out of curiosity I calculated the mass as 3.1696 x 10^32 kilograms.
I trust you calculated the same thing?
Anyway, I was glad to help out.

shk
Just out of curiosity I calculated the mass as 3.1696 x 10^32 kilograms.
I trust you calculated the same thing?
Anyway, I was glad to help out.
yes I have got the same value . Many thanks. I was worried that my answer was wrong but now with your help I'm confident that it's correct. Thanks for the great help

wolf1728
Gold Member
Glad to help!! That's why we're here.