Question

If the earth had twice its present radius and twice its present mass, what would happen to your weight? Explain. What is the relationship between the radius (R) of orbit of a satellite and its period (T)?

Answer 1

currently we have: g=G*(m_earth*m_yours)/r_earth^2 g=9.8 m/s^2 G=constant which doesn't matter in terms of your question so we're going to throw it out m=mass So we are looking for a ratio g_new/g=(m_earth new/m_earth)*(m_yours new/m_yours)/(r_earth new/r_earth)^2 Now your mass doesn't change so m_yours cancels g_new/g= 2/(2)^2 or g_new/g=1/2 you would feel half the current acceleration from gravity that you do now, so you would weigh half as much as you currently do. Explain: Newton says so. Pretty much the relationship for gravitational pull is linear for mass but squared for distance. So changes in distance between objects becomes much more important than changes in the mass of the two objects. Relationship between Radius and Period of a satellite: T~R^(3/2)