Dynamic Sun that directly or indirectly controls the whole geospace environment and affects the space-borne (satellites, rockets) and ground based technological systems (communication, navigation). Numbers of sunspots seen on the solar surface are known as the measure of solar activity. By tracking these sunspots we have calculated solar rotational time period (synodic and sidereal time period). To that end, we have used the unique facility of a solar telescope, a CCD camera and a solar spectrometer installed at Physics Department, Banaras Hindu University, Varanasi. We observed full solar disc images during morning hours (9:15 am to 9:30 am) from April, 8-18, 2019. The synodic time period and the sidereal time period were calculated as 26.94 days and 25.09 days respectively. It is also observed that the solar disc intensity also known as solar limb darkening effect decreases from center to the limb. To study the solar limb darkening effect, we have taken full solar disk images free from sunspots during morning hours from 28 th March, 2019 to 8 th April, 2019 and analyzed their intensity variations to calculate solar limb darkening coefficient of the Sun. The average solar limb darkening coefficient comes out to be 0.61. Our above observed results are found to be in consistent with the other reported results.