Mean solar day is the time interval between two successive noons when the sun passes through the zenith point (meridian). $A$ sidereal day is the time interval between two successive transits of a distant star through the zenith point (meridian). By drawing an appropriate diagram showing the earth's spin and orbital motion,show that the mean solar day is $4\,\text{min}$ longer than the sidereal day. In other words,distant stars would rise $4\,\text{min}$ early every successive day.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Every day,the Earth advances in its orbit by approximately $1^{\circ}$.
To have the sun at the zenith point again,the Earth must rotate by $361^{\circ}$ (which we define as $1$ mean solar day).
Since $361^{\circ}$ corresponds to $24\,\text{h}$,we can calculate the time taken for $1^{\circ}$ as follows:
$\because \text{To cover } 361^{\circ}, \text{time taken} = 24\,\text{h}$
$\because \text{To cover } 1^{\circ}, \text{time taken} = t$
$t = \frac{24}{361} \times 1 \approx 0.0664\,\text{h}$
$t = 0.0664 \times 60\,\text{min} \approx 3.99\,\text{min} \approx 4\,\text{min}$.
Hence,the mean solar day is $4\,\text{min}$ longer than the sidereal day,and distant stars rise $4\,\text{min}$ early every successive day.

Explore More

Similar Questions

Assume that a tunnel is dug along a chord of the Earth,at a perpendicular distance $(R / 2)$ from the Earth's centre,where $R$ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel,it will execute a simple harmonic motion with a time period:

Identify the correct option.

If the height of a satellite from the surface of the Earth is increased,then its

Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same direction because of their mutual gravitational attractive force. The velocity of a particle is given by

Difficult
View Solution

$A$ spacecraft travels in a straight line from the Earth to the Moon. How will its weight change during this journey?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo