An unmanned satellite A and a spacecraft B are orbiting around the earth in the same circular orbit as shown. The spacecraft is ahead of the satellite by some time. Let us consider that some technical problem has arisen in the satellite and the astronaut from B has made it correct. For this to be done docking of two (A and B) is required (in layman terms connecting A and B). To achieve this, the rockets of A have been fired in forward direction and docking takes place as shown in the figure below: Take mass of the earth =5.98xx10^(24)kg Radius of the earth =6400 km Orbital radius =9600km Mass of satellite A=320 kg Mass of spacecraft =3200 kg Assume that initially spacecraft B leads satellite A by 100s, i.e., A arrives at any particle position after 100 s of B’s arrival. Based on the above information answer the following questions. By doing the above operation, now by how much time is the satellite leading the spacecraft?

An unmanned satellite A and a spacecraft B are orbiting around the ear

1.	An unmanned satellite A and a spacecraft B are orbiting around the earth in the same circular orbit as shown. The spacecraft is ahead of the satellite by some time. Let us consider that some technical problem has arisen in the satellite and the astronaut from B has made it correct. For this to be done docking of two (A and B) is required (in layman terms connecting A and B). To achieve this, the rockets of A have been fired in forward direction and docking takes place as shown in the figure below: Take mass of the earth =5.98xx10^(24)kg Radius of the earth =6400 km Orbital radius =9600km Mass of satellite A=320 kg Mass of spacecraft =3200 kg Assume that initially spacecraft B leads satellite A by 100s, i.e., A arrives at any particle position after 100 s of B’s arrival. Based on the above information answer the following questions. By doing the above operation, now by how much time is the satellite leading the spacecraft?
Answer» `38s` `138s` Lags by `38 s` Lags by `138 s` SOLUTION :Initially the time periods of the satellite and the spacedraft were same equal to `9358 s` and after firing rockets of `A`, it acquires, slower and faster orbit and `A` will come to initial POSITION in time PERIOD of `9220 s` while `B` will take `9358 s` to come to its initial position or `(9358-100)s` to come to the ORIGINAL position of `A` as `100 s` is the initial time gap between the two. It means now `A` LEADS `B` by `(9358-100-9220)=38s`.