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- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/08%3A_C8)_Conservation_of_Energy-_Kinetic_and_Gravitational/8.03%3A_Universal_GravityThe situation we want to understand is the gravitational interaction near the Earth - in fact, very near the Earth, so that we can write the height of the object from the surface h is much smaller...The situation we want to understand is the gravitational interaction near the Earth - in fact, very near the Earth, so that we can write the height of the object from the surface h is much smaller than the radius of the Earth, h<<RE.
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/08%3A_C8)_Conservation_of_Energy-_Kinetic_and_Gravitational/8.03%3A_The_Inverse-Square_LawHere I have put a subscript E on g to emphasize that this is the acceleration of gravity near the surface of the Earth, and that the same formula could be used to find the acceleration of grav...Here I have put a subscript E on g to emphasize that this is the acceleration of gravity near the surface of the Earth, and that the same formula could be used to find the acceleration of gravity near the surface of any other planet or moon, just replacing ME and RE by the mass and radius of the planet or moon in question.
- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/13%3A_Application_-_Orbits_and_Kepler's_Laws/13.01%3A_OrbitsAll the initial velocity vectors in the figure have the same magnitude, and the release point (with position vector →ri) is the same for all the orbits, so they all have the same energy; inde...All the initial velocity vectors in the figure have the same magnitude, and the release point (with position vector →ri) is the same for all the orbits, so they all have the same energy; indeed, you can check that the semimajor axis of the two ellipses is the same as the radius of the circle, as required by Equation (???).
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_I_-_Classical_Mechanics_(Gea-Banacloche)/10%3A_Gravity/10.01%3A_The_Inverse-Square_LawSuppose that, at some time tA, the particle is at point A, and a time Δt later it has moved to A′ . The area “swept” by its position vector is shown in grey in the figure, a...Suppose that, at some time tA, the particle is at point A, and a time Δt later it has moved to A′ . The area “swept” by its position vector is shown in grey in the figure, and Kepler’s second law states that it must be the same, for the same time interval, at any point in the trajectory; so, for instance, if the particle starts out at B instead, then in the same time interval Δt it will move to a point B′ such that the area of the “curved triangl…
- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/13%3A_Application_-_Orbits_and_Kepler's_Laws/13.02%3A_Kepler's_LawsThe area “swept” by its position vector is shown in grey in the figure, and Kepler’s second law states that it must be the same, for the same time interval, at any point in the trajectory; so, for ins...The area “swept” by its position vector is shown in grey in the figure, and Kepler’s second law states that it must be the same, for the same time interval, at any point in the trajectory; so, for instance, if the particle starts out at B instead, then in the same time interval Δt it will move to a point B′ such that the area of the “curved triangle” OBB′ equals the area of OAA′.
