Question

6 of 13 Properties of Circular Orbits Constants Find the orbital speed of a satelite in a circular orbit of radius R around a planet of mass M. Express the orbital speed in terms of G, M, and R. View Available Hint(s) Learning Goal: To find some of the parameters characterizing an object moving in a circular orbit. The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit: a circular one. This problem concerns the properties of circular orbits for a satelite orbiting a planet of mass M 190 Axo th ? E XV V 121 x.100 . For all parts of this problem, where appropriate, use for the universal gravitational constant. Submit Previous Answers X Incorrect; Try Again; 2 attempts remaining

Answer 1

Answer:

Gileen Mass ам = m. Mass another object = cm of object f potential energy of object=U We know that universal gravitational constant Gi. Intially, We will obtain gravitational force acting ow the object F = G.m.m R2 At the same time, centrifugad force acting on a body is given by F = mos R Equating both the G.mm forces & solve for orbital speed &. = m. 162 R 10 = Gm VR orbild GM satilice (Answer) Speed & of R Kinetic satilete with mass m ina cuceler energy 'k' f Orbit with radius & is given by Kinetic energy KE = 2 m 2 mee - 2xKE m G71 R = 2X KE → KE = Gum 2R KE = GMm 2R (Answer) velocity of the satilite, v= 21TR whese T=cobital speed 21TR T 2TR T on both sides R squassing Gm (217R) ² 2 = (25R)? T2 4T R3 (Ansoes) Gm RO IT Gm 2 TUR

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