# Determine the mass of the star?

• ohheytai
In summary, the conversation discusses using the equations (-G*m1*m2)/r^2 and dP/dt to find the mass of a planet in orbit. The conversation also mentions the use of vectors and the importance of understanding the relationship between centripetal and gravitational forces.
ohheytai

(-G*m1*m2)/r^2
dP/dt

## The Attempt at a Solution

I don't even know where to start i drew everything out and i think dP/dT is 0 cause its at a constant speed someone please help! :(

#### Attachments

• Written Problem 6.pdf
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At constant speed in circular motion, acceleration would be constant towards the centre, creating the centripetal force, Fc.

In the case of orbit, Fc = Fg = GMstarMplanet / R2

R, T and G are given, so all you need to do is to derive the mass of the planet in terms of the given quantities.

Rearranging the expression to find star's mass, I get:
Mstar = Fc R2 / G Mplanet

The only unknowns left will be Fc and mass of planet.

However, it is known that Fc = Mplanet v2 / R. Thus, the mass of planet in Fc can be canceled with the mass of planet in my arranged expression above to give:

Mstar = v2 R / G

v = 2pi R / T (given in question as well), thus, final expression being:

Mstar = 4 pi2 R 3 / G T 2

This is just my first try. please let me know if I've made any errors or if you disagree.

is it possible to do this without centripetal force? and using vectors?

Dimension for G is m3 kg-1 s-2, making the overall expression's dimension kg as well. So my expression SHOULD be correct.

ohheytai said:
is it possible to do this without centripetal force? and using vectors?

The purpose of this problem is to emphasize that in an orbit, the centripetal force is the gravitational force, and thus using simple algebra, master the variables of the expression for Fg.

Vectors will point only the tangential velocity and Fc, but to determine the mass, you need expression for Fg.

okay thank youuu!

## 1. How do you determine the mass of a star?

To determine the mass of a star, scientists use a combination of observational data and theoretical models. They take into account factors such as the star's luminosity, temperature, and spectral type to estimate its mass.

## 2. Why is determining the mass of a star important?

Determining the mass of a star is important because it provides crucial information about the star's evolution, lifespan, and eventual fate. It also helps us understand the overall structure and dynamics of the universe.

## 3. Can the mass of a star change over time?

Yes, the mass of a star can change over time. As a star burns through its fuel, it can lose mass through nuclear fusion reactions. Additionally, external factors such as interactions with other stars can also affect a star's mass.

## 4. How accurate are the methods used to determine a star's mass?

The methods used to determine a star's mass are generally accurate within a certain range. The accuracy depends on the quality of the observational data and the reliability of the theoretical models used. However, there is always a margin of error in any scientific measurement.

## 5. Can we determine the mass of a star in other galaxies?

Yes, we can determine the mass of a star in other galaxies using similar methods as those used for stars in our own galaxy. However, the distance and resolution of the observations may affect the accuracy of the measurement.

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