00:02
In this problem we have two satellites in different orbits around the earth and we have to find the ratio of their potential energy and the ratio of kinetic energy.
00:14
So for any satellite in orbit around a planet the gravitational force provides the centripetal force.
00:24
So the gravitational force fg will be equal to centrifugal force f .c gravitational force by earth is g m capital m is mass of earth and small m is a mass of satellite upon r square where r is radius of orbit and centripetal force will be m v square upon r where v is speed in orbit and r is radius of orbit so this gives us m v square equal to g m m upon r now kinetic energy is k equal to half mv square equal to half mv square is g m m upon r so this is g m upon 2 r so this is the equation for kinetic energy for a satellite of mass m in orbit of radius r around earth potential energy is minus g m m m upon r so the ratio of potential energies of satellite b to satellite a will be p e b upon p e a minus g m m both have same mass upon r b this is the radius of orbit for b and this is potential energy for b and potential energy for a is minus g m m upon r a which is the radius of orbit of a so this gives us r a upon r b now r b r a is radius of orbit of a, so it will be equal to ha, the altitude of satellite a plus radius of earth, capital r.
02:30
Similarly, radius of orbit for b will be hb, which is the altitude of satellite b plus radius, radius of earth r.
02:43
Value of ha is 5 ,850 km plus radius of earth is 6 ,370 kilometers upon altitude of b is 15 ,500 kilometer plus 670 kilometers so this gives the ratio of potential energy is equal to 0 .559.
03:21
For the second part we have to find the ratio of kinetic energies.
03:27
So the ratio is kinetic energy of b to kinetic energy of a.
03:34
Now we saw in part one that kinetic energy expression is gmm upon 2r.
03:42
So here it will have gm small m upon 2r b upon gm small m upon 2ra.
03:53
So again this gives us r a upon r b just like the ratio of potential energies and so we directly write the result 0 .559 which we found in part a.
04:13
Here we have to find in part c which satellite has greater total energy total energy is e equal to kinetic energy plus potential energy kinetic energy is minus g sari gmm upon 2r plus potential energy is minus gmm upon r and this is equal to gmm upon r 1 upon 2 minus 1 and this will be equal to minus gmm m upon 2r so this is the expression for total energy now the capital and mass of earth and the small m mass of satellite is same for both the satellites.
05:05
The radius of orbit is different...