Given the mass of a star, determine Kepler's constant.

[Solidearth]

Homework Statement

"The mass of a star is 4.85x10^29kg. In scientific notation, Kepler's constant for that star is bx10^w s²/m³. the value of b is_____."

Homework Equations

K=T²/r³

The Attempt at a Solution

This problem is very tough. I first assumed that K would be 0 because the star has no satellites, and therefore is experiencing linear motion, not circular motion. To my dismay however, the answer is indeed 3 digits and K_star> 0.
The greatest obstacle is how am I to derive the period and semi major axis of its orbit, if i am only given the star's mass?!
Any insights into this problem are helpful.
Thanks!

 

[LowlyPion]

Homework Statement

"The mass of a star is 4.85x10^29kg. In scientific notation, Kepler's constant for that star is bx10^w s²/m³. the value of b is_____."

Homework Equations

K=T²/r³

The Attempt at a Solution

This problem is very tough. I first assumed that K would be 0 because the star has no satellites, and therefore is experiencing linear motion, not circular motion. To my dismay however, the answer is indeed 3 digits and K_star> 0.
The greatest obstacle is how am I to derive the period and semi major axis of its orbit, if i am only given the star's mass?!
Any insights into this problem are helpful.
Thanks!

Welcome to PF.

If K = T²/ a³

Can't you determine K directly from:

T = 2π*(a³/GM)^1/2

Yielding

K = 4π²/(G*M)

 

[nlightner]

Dear student,

First of all, it is important to note that Kepler's constant is not dependent on the presence or absence of satellites. It is a constant that relates the period and semi-major axis of an orbit to the mass of the central body, in this case, the star.

To determine Kepler's constant, we can use the equation K=T^2/r^3, where T is the period of the orbit and r is the semi-major axis. In this case, we are given the mass of the star (4.85x10^29kg), but we do not have information about the period or semi-major axis.

To solve for K, we need to find the period and semi-major axis of the orbit. This can be done by observing the motion of objects around the star, such as planets or other celestial bodies. We can also use other methods, such as radial velocity measurements, to determine the period and semi-major axis.

Once we have the values for T and r, we can plug them into the equation K=T^2/r^3 to solve for K. Therefore, without any additional information about the star's orbit, we cannot determine Kepler's constant. It is important to have multiple pieces of information to accurately calculate this constant.

I hope this helps clarify the problem for you. Keep in mind that in science, we often need to gather multiple pieces of information and use various methods to solve a problem. Good luck with your studies!