Calculating semi-major axis and minimum mass of an exoplanet

In summary, the conversation discusses the calculation of minimum mass and semi-major axis for an unknown planet using Kepler's third law and given data. The results are found to be 0.037 AU for the semi-major axis and 7.696 Mjupiter for the minimum mass. The speaker is also seeking help in calculating the uncertainties for these values.
  • #1
Mauro Montemayor
1
0
Hello guys,

I'm doing my physics coursework on kepler's third law and I'm finding the minimum mass and semi-major axis of a unknown planet. I have the following data:

Stellar mass Mstar = 1.31 ± 0.05 Msun

Orbital period P = 2.243752 ± 0.00005 days

Radial velocity semi-amplitude: V = 993.0 ± 3 m/s

Inclination i = 84.32º ± 0.67

We assume eccentricity e=0

Gravitational constant, G=6.67408 × 10-11 m3 kg-1 s-2

Jupiter mass: Mj=1,898 × 10^27 kg

From this I found that,
semi-major axis = 5.49042 x 10^9 m = 0.037 AU
Minimum mass = 1.46082 x 10^28 kg = 7.696 Mjupiter

The results are correct. However, I am not able to find the uncertainties of these two values. I would appreciate some help with this matter.

Thank you,

Mauro
 
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  • #2
Hi Mauro:

If you show the actual calculations that you used to derive semi-major axis and Minimum mass, I think that I can show you how to calculate the uncertainties.

Regards,
Buzz
 

1. What is the semi-major axis of an exoplanet?

The semi-major axis of an exoplanet is the distance between the planet and its parent star, measured from the center of the star to the center of the planet. It is one of the key parameters used to characterize an exoplanet's orbit.

2. How is the semi-major axis of an exoplanet calculated?

The semi-major axis can be calculated using Kepler's third law, which states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. By measuring the orbital period of the exoplanet and the mass of its parent star, scientists can calculate the semi-major axis.

3. What is the minimum mass of an exoplanet?

The minimum mass of an exoplanet is the lower limit of its mass, as determined by the radial velocity method. This method measures the slight wobble of a star caused by the gravitational pull of an orbiting planet. The more massive the planet, the larger the wobble, and the easier it is to detect. Therefore, the minimum mass is the smallest mass that can be detected.

4. How is the minimum mass of an exoplanet calculated?

The minimum mass is calculated using the radial velocity method, which measures the star's wobble caused by the gravitational pull of an orbiting planet. The more massive the planet, the larger the wobble, and the easier it is to detect. Scientists use this data to calculate the minimum mass of the planet.

5. Why are the semi-major axis and minimum mass important parameters for exoplanets?

These parameters provide valuable information about an exoplanet's orbit and size. The semi-major axis helps determine the distance of the planet from its parent star, which is crucial for understanding its habitability. The minimum mass gives us an idea of the planet's size and composition, providing insights into its potential for supporting life. These parameters also help scientists classify and compare different exoplanets, aiding in the search for habitable worlds beyond our solar system.

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