You are given the following data from observations of an exoplanet: Using Kepler’s Third Law (r3 = MT2 where M is the mass of the central star) find the orbital radius in astronomical units of this planet. M = 1.5 times the mass of the sun. Remember to convert days to years using 365.25 as the length of a year in days. What is the semimajor axis of this planet in AU? - Knowing the orbital radius in both kn and AU, use the value in km to find the circumference of the orbit, then convert that to meters. (Assume the orbit is a perfect circle). - Knowing the orbital circumference and the period in days, convert the days to seconds (multiply by 86,400) and find the orbital velocity in m/s
You are given the following data from observations of an exoplanet: Using Kepler’s Third Law (r3 = MT2 where M is the mass of the central star) find the orbital radius in astronomical units of this planet. M = 1.5 times the mass of the sun. Remember to convert days to years using 365.25 as the length of a year in days. What is the semimajor axis of this planet in AU?
- Knowing the orbital radius in both kn and AU, use the value in km to find the circumference of the orbit, then convert that to meters. (Assume the orbit is a perfect circle).
- Knowing the orbital circumference and the period in days, convert the days to seconds (multiply by 86,400) and find the orbital velocity in m/s
- With that orbital velocity, the radius of the orbit in meters, find the centripetal acceleration of our exoplanet
- Knowing the acceleration that our planet experiences, calculate the force that the host star exerts on the planet
- Knowing the force on the planet, the orbital radius, and the mass of the parent star, use the equation for gravitational force to find the mass of our planet (m2). (To get m1 in kg multiply the mass of the star in solar masses by 1.98 x 1030)
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