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

$A$ large spherical mass $M$ is fixed at one position and two identical point masses $m$ are kept on a line passing through the centre of $M$ (see figure). The point masses are connected by a rigid massless rod of length $\ell$ and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to $M$ is at a distance $r = 3\ell$ from $M$,the tension in the rod is zero for $m = k\left(\frac{M}{288}\right)$. The value of $k$ is

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

$A$ particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement is

Difficult
View Solution

If the distance of Mercury from the Sun is $0.4$ times the distance of the Earth from the Sun,find the solar constant of Mercury in $cal/min \cdot cm^2$. The solar constant of the Earth is $2 \, cal/min \cdot cm^2$.

Difficult
View Solution

If a tunnel is cut at any orientation through the Earth,a ball released from one end will reach the other end in time ........ $\text{min}$ (neglect Earth's rotation).

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