Kepler's First Law Practice Problems

NASA's TESS found in 2020 an unusual gas giant exoplanet, TOI-2109 b, that orbit an F-type star. TOI-2109 b needs 16 hours, the shortest ever measured for a gas giant exoplanet, to complete one orbit around its parent star. TOI-2109 b mean distance from its star is 2.67 × 10⁶ km. How fast, in Km/s, is this planet moving?

The planet Kepler-186f, known as the Earth's cousin, is located about 500 light-years from Earth in the constellation Cygnus. Kepler-186f orbits about 52.4 million kilometers from its red dwarf star. The mass of a red dwarf star is about 0.48 M_s. M_s is the mass of the sun. Determine i) the orbital speed and ii) the orbital period of the Kepler 186f planet.

Kepler-36b and Kepler-36c are two highly close planets orbiting around their parent star, Kepler-36. Kepler-36b has an orbital period of 13.9 days and its mean orbital radius from Kepler-36 is 0.1153 AU. The orbital period for Kepler-36c is 16.2 days. Presume that the two planets have no effect on one another. Calculate Kepler-36c's orbital distance (r_Kepler-36c ) in the atmospheric unit (AU) without using the mass of the parent star.

One of the aims of the Kepler mission is to discover "small" sized planets in our galaxy. The planet Kepler 5b was discovered early in the mission. It travels around its parent star with a mean orbital radius of 7,580,000 km while the period is 3.55 days. Use this data to calculate the mass of the parent star in kilograms and in terms of the mass of our sun.