# Mass of a star given orbital radius and period

• disque
In summary, the conversation discusses finding the mass of a star based on the orbital radius and period of a planet around it. The equation for centripetal force and Kepler's third law are mentioned as possible methods to solve the problem. It is suggested to ignore the mass of the planet in this calculation.
disque

## Homework Statement

In recent years, a number of nearby stars have been found to possesses planets. Suppose, the orbital radius of such a planet is found to be 4.3 times 1011 m, with a period of 1080 days. Find the mass of the star.

?

## The Attempt at a Solution

I don't even know where to start with this question. Without the mass of the planet I am clueless. ANy help would be much appreciated, Thanks a lot.

disque said:

## Homework Statement

In recent years, a number of nearby stars have been found to possesses planets. Suppose, the orbital radius of such a planet is found to be 4.3 times 1011 m, with a period of 1080 days. Find the mass of the star.

?

## The Attempt at a Solution

I don't even know where to start with this question. Without the mass of the planet I am clueless. ANy help would be much appreciated, Thanks a lot.
Let's start by looking at what interactions are relevant. So erm what are the relevant interactions? Or more to the point, what forces are acting on our planet?
After that we'll need to see what the motion of the planet means in terms of forces. So again can you think of a relation between the period, mass and radius for an object in circular motion to the force exerted on it?
after that we should be at a point to get an answer after a bit of algebra

(mv^2)/r
am i on the right track?

disque said:
(mv^2)/r
am i on the right track?

So that's the equation for the centripetal force, you will need to relate v to the period and radius. Also you need to recognize what force is causing the circular motion and what the equation for that force is

Look up "Kepler's third law" in the index of your book. You are given numbers to substitute into the formula.

I'm surprised they've not covered Kepler's laws first? Did you skip a chapter?

Seems a little advanced to expect you to know how to find mass without it?

You don't really need to know the mass of the planet since it will be much smaller than the star generally so you can approximate it ignoring the planets mass to all intents and purposes.

Even Jupiter's mass is only ~1/1000 of the Suns.

Last edited:

## 1. What is the equation for calculating the mass of a star given orbital radius and period?

The equation for calculating the mass of a star given orbital radius and period is M = (4π²r³)/G(T²), where M is the mass of the star, r is the orbital radius, T is the orbital period, and G is the gravitational constant.

## 2. Can the mass of a star be determined using only the orbital radius and period?

Yes, the mass of a star can be determined using only the orbital radius and period, as long as the orbital radius is known and the period is measured accurately. This is possible due to Kepler's Third Law, which states that the ratio of the cube of the orbital radius to the square of the orbital period is constant for all objects orbiting the same star.

## 3. How does the mass of a star affect its orbital radius and period?

The mass of a star directly affects the orbital radius and period of objects orbiting around it. The more massive the star, the larger the orbital radius and longer the orbital period will be for objects orbiting it. This is because the gravitational force between the star and the orbiting object is stronger for more massive stars, causing the object to have a wider orbit and longer period.

## 4. What units are used to measure the mass of a star?

The mass of a star is typically measured in units of solar masses (M☉), which is equal to the mass of our Sun. For example, a star with a mass of 2M☉ would have twice the mass of our Sun.

## 5. Are there any other factors that can affect the mass of a star given orbital radius and period?

There are other factors that can affect the mass of a star given orbital radius and period, such as the presence of other nearby stars or the influence of dark matter. However, these effects are typically small and can be accounted for in more complex equations or through observational data.

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