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

In summary, the conversation discusses the value of Kepler's constant for a star with a mass of 4.85x10^29kg. The equation for Kepler's constant is given as K=T2/r3, but the period and semi-major axis of the star's orbit are not provided. Despite initial assumptions, the value of K is not zero and the greatest obstacle is determining the period and semi-major axis with only the star's mass given. The value of K can be determined using the equation T = 2π*(a3/GM)1/2.
  • #1

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 Kstar> 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!
 
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  • #2
Solidearth said:

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 Kstar> 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)
 
  • #3


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!
 

What is Kepler's constant?

Kepler's constant is a mathematical value used in the calculation of orbital periods of objects orbiting a central body, such as planets orbiting a star. It is denoted by the symbol "k" and has a value of approximately 0.01720209895.

How is Kepler's constant related to the mass of a star?

Kepler's constant is related to the mass of a star through the formula k = √(G * M), where G is the gravitational constant and M is the mass of the star. This means that the larger the mass of the star, the larger the value of k will be.

What is the unit of measurement for Kepler's constant?

Kepler's constant is typically measured in units of days per astronomical unit cubed, or days per AU^3. This unit is commonly used in astronomy for measuring orbital periods or the time it takes for an object to complete one orbit around another object.

Can Kepler's constant be used for any type of star?

Yes, Kepler's constant can be used for any type of star as long as its mass is known. This includes main sequence stars, white dwarfs, and even black holes. However, it may not be applicable for extremely massive objects such as supermassive black holes.

How is Kepler's constant used in the study of exoplanets?

Kepler's constant is used in the study of exoplanets to calculate their orbital periods and distances from their host star. This information can then be used to determine other characteristics of the exoplanet, such as its size and composition. It is also useful in predicting the presence of other planets in the same system.

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