Question

What is the length of of one sidereal day in terms of solar days? What is it in terms of hours, minutes and seconds (in the format hh:mm:ss)? Note that a mean solar day has, of course, 24 hours. (b) You are planning to take the photos demonstrating apparent motion of Jupiter. You placed a photo camera on an immovable tripod, on which it will stay for the duration of observations. You want to take the first photo on September 15, 2019 at 9:00:00 pm. At what time you’d take another photo on September 16 in order to have all stars in exactly the same position as in the first shot (so that you can see the motion of the planet relative to the stars)? (c) You want to take another every day till September 30, again with all stars at the same position as before. At what time are you going to take the photo on the last day of observations?

Answer 1

a. Length of One sidereal day = 0.9972 Solar Day or 23:56:04 Hours

b. On September 16 the photo should be taken at 08:56:04 pm

c. On September 30, the photo should be taken at 08:01:00 pm

Step-by-step explanation:

Sidereal Day: It is the time the Earth takes to complete one rotation with respect to distant stars. This duration is 23:56:04 Hrs.

Solar Day: It is the time the Earth takes to complete one rotation with respect to the Sun. This duration is 24 Hours. This difference of around 03:56 Minutes occur due to revolution of Earth around the Sun. As Earth rotates, it also moves in the orbit around the Sun. Because of this the Earth will need to rotate extra to complete the rotation with respect to the Sun. Since, stars are very far from us, this revolution around the Sun doesn't have any impact on Sidereal day.

The time that we use is based upon the Sun. So if we need to observe the stars at the same point again we will need to follow sidereal time which is 03:56 minutes faster. Simply put you will need to go back 03:56 minutes per day for the star to be at the same point. Thus on September 16 the photo should be taken at 08:56:04 pm and on September 30, the photo should be taken at 08:01:00 pm.