4 Now let s look at how everything you ve seen so far fits

Last updated: 4/26/2023

4 Now let s look at how everything you ve seen so far fits together to make the standard equation Using data for individual exoplanets you found a xwhere r is the distance from the star to a planet Another way to say this A where AR is the slope of the graph and what we called the acceleration ratio is a In this section you saw AR x m where my is the mass of the star Since the slope of the graph you made is also called G we can also say AR Gm When we combine that with what you found using individual exoplanets we get ac The equation is usually written in terms of force rather than acceleration Since the centripetal acceleration of an exoplanet is caused by the force of gravity on the exoplanet by the star then F m a where me is the mass of the exoplanet This becomes the standard equation mym This equation is often called the Universal Gravitation equation and works to find the force of gravity between any two objects not just a star and a planet 5 Let s try applying this equation to predict the acceleration due to gravity near Earth s surface The mass of Earth is 5 972 x 10 0 kg and the radius of Earth is 6 371 x 10 m According to the universal gravitation equation what should be the acceleration due to gravity near Earth s surface m s