Question

NASA’s newest exoplanet-hunting telescope, the Transiting Exoplanet Survey Satellite (TESS), has now found its first Earth-sized world. This is another exciting step towards finding worlds beyond our solar system that might be capable of supporting life. The planet – labeled HD 21749c – orbits the star HD 21749, about 52 light-years from Earth. a) What is the force between this planet and its star? The planet has a mass of kg, the star a mass of kg, and the distance the planet orbits the star is m. b) If the radius of the planet is 4842 km then what is the gravitational acceleration on the planet?

Answer 1

The force between the planet and the star can be found by Newton's law of universal gravitation

$$F=G\frac{m_pm_s}{r^2}=\\ \space\\=6.673\cdot10^{-11}\frac{(3.7\cdot6\cdot10^{24})(0.68\cdot2\cdot10^{30})}{(0.0695\cdot149.6\cdot10^6)^2}=1.86\cdot10^{31}\text{ N}.$$

The gravitational acceleration on the planet can be found by the equilibrium of forces acting on a body on the planet's surface:

$$G\frac{m_pm_b}{R^2}=m_bg,\\ \space\\ g=\frac{Gm_p}{R^2}=63.2\text{ m/s}^2.$$

Quite too much for human beings.