# Mass of stars companion from radial velocity

• ChrisBaker8
In summary, the solar-like star HD209458 has a companion with a mass of 6.154 x 10^26 kg, making it a large planet, possibly a Hot Jupiter. The mass was calculated using Kepler's third law and the given information about the period and radial velocity variations.
ChrisBaker8

## Homework Statement

The solar-like star HD209458 with a mass of 1.14 solar masses exhibits radial velocity variations with a period of 3.52 days and an amplitude of 84m/s. What is the mass of its companion and what type of object is it?

## Homework Equations

M/m = r/R = v/V

[M,R,V = star, m,r,v = companion]

## The Attempt at a Solution

I've just worked this out myself so if it's off please tell me, but I have to assume the star and planet (or body) are both moving in circular orbits, and the are on opposite sides of the centre of mass, and rotating around it in their orbits (stars one much smaller) with equal periods, as shown in this clip:

http://en.wikipedia.org/wiki/File:Planet_reflex_200.gif

Now, I'm assuming the data given means that (in the above animation, assuming the viewer is to the left of the centre of mass at infinity) the star will be moving 42m/s faster towards the observer (or 42m/s slower away from the observer, to be more accurate) at the bottom of the orbit, and 42m/s faster away from the observer at the top of the orbit.

The orbit of both takes 3.52 days. So if I know the star is traveling (forgetting the whole system is moving) at 42m/s around the circle, and I know the period, I can calculate the circumference and therefore radius of the stars orbit. But from there I don't know. The companion could be close and large, or far away and small. I'm not sure how I can work this out.

Sounds reasonable, I'm guessing you have to assume that it's not an eclipsing binary and you have to that it's orbiting it's compact companion.

I'm not sure what that means. I still have no way of working out the mass of the companion. It could be the same size/mass of the star and an equal radius away on the other side, or it could be a much smaller planter and further away, like in the animations. How can I tell which is the case if the question is looking for the mass of the companion?

I know M, R and V but not m, r or v

i think you are over-thinking the question and should just assume it is a circular orbit around a more massive companion.

I... assume the star is orbiting around an unmoving (within the system) object of infinite mass? ?

I don't see you have the info to do anything else !

Keplers third law period = sqrt ( 4 pi^2 r^3 / GM )
You can get r from the radial speed and period.

period = sqrt ( 4 pi^2 r^3 / GM )

304128 s = $$\sqrt{(4\pi^{2}r^{3})/(6.673.10^{-11}.M)}$$

Is this using M as the given star mass and r as the radius of the orbit of its companion?

Is this using M as the given star mass and r as the radius of the orbit of its companion?

Yes. M is the mass of the central star, R is the radius of the object orbiting around it. This formula is just a result of Newton's Law of Gravitation.

right, I used K3L to work out r, which was 7.078 x 10^9 m

therefore mass of companion = 6.154 x 10^26 kg

this makes it what...a big planet? Jupiter is x10^27, so I'll assume so

wait this makes the body a Hot Jupiter, doesn't it?

## What is the mass of a star's companion based on its radial velocity?

The mass of a star's companion can be calculated using Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. By measuring the orbital period and the semi-major axis, the mass of the companion can be determined.

## How does radial velocity affect the mass of a star's companion?

The radial velocity of a star is caused by the gravitational pull of its companion. The more massive the companion, the greater the radial velocity of the star will be. This means that a higher radial velocity corresponds to a higher mass for the companion.

## What is the significance of determining the mass of a star's companion from radial velocity?

Determining the mass of a star's companion from radial velocity is important for understanding the dynamics of a binary star system. It also provides valuable information about the physical properties and evolution of the companion star.

## What are the limitations of using radial velocity to determine the mass of a star's companion?

Radial velocity measurements can only provide an estimate of the minimum mass of the companion, as the true mass may be higher if the orbit is inclined or if there are additional sources of acceleration. Other factors, such as stellar activity and instrumental noise, can also affect the accuracy of the measurement.

## How do scientists use radial velocity data to study the distribution of binary stars in the galaxy?

By analyzing the radial velocity data of a large sample of binary stars, scientists can determine the distribution of binary stars in the galaxy and gain insights into the formation and evolution of these systems. This can also help in identifying potential exoplanet-hosting stars and detecting unseen companions in binary systems.

• Introductory Physics Homework Help
Replies
6
Views
732
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
3K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Astronomy and Astrophysics
Replies
14
Views
2K