You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Universal Law of Gravitation

A planet of m...

Question

A planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The time period of the planet is proportional to:

r_{1}^{3 / 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{2}^{3 / 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{r_{1} + r_{2}}{2})^{3 / 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{(r_{1} - r_{2})^{3 / 2}}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(\frac{r_{1} + r_{2}}{2})^{3 / 2}$
According to Kepler's law,
$T^{2} \propto a^{3}$
Here, a $=$ semi-major axis $= (\frac{r_{1} + r_{2}}{2})$
$∴ T^{2} \propto (\frac{r_{1} + r_{2}}{2})^{3}$
$\Rightarrow T \propto (\frac{r_{1} + r_{2}}{2})^{3 / 2}$

Suggest Corrections

Similar questions

Q. A planet of mass

m

is moving in an elliptical orbit about the Sun (mass of Sun =

M

). The maximum and minimum distances of the planet from the Sun are

r_{1}

and

r_{2}

respectively. The period of revolution of the planet will be proportional to:

Q. A planet of mass m moves around the Sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the Sun are

r_{1}

and

r_{2}

, respectively. Find the relation between the time period of the planet in terms of

r_{1}

and

r_{2}

Q. The time periods and the mean radii of the orbits of two planets around Sun are

T_{1}, T_{2} a n d r_{1}, r_{2}

respectively. The ratio

\frac{T_{1}}{T_{2}}

is equal to .

Q. A planet of mass

m

moves in an elliptical path around the Sun so that its maximum and minimum distance from the sun are equal to

r_{1}

and

r_{2}

respectively. Find the angular momentum of this planet relative to the center of the sun. Mass of the sun is

M

When a planet orbiting around the sun an elliptical orbit R1 and R2 are the closest and farthest distance from the sun Then the ratio of the magnitudes of maximum and minimum gravitational forces between them is

A.r1:r2

B.r2:r1

C.r1^2:r2^2

D.r2^2:r1^2

Join BYJU'S Learning Program

A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distances of the planet from the sun are r1 and r2 respectively. The time period of the planet is proportional to:

The correct option is C (r1+r22)3/2According to Kepler's law,T2∝a3Here, a = semi-major axis =(r1+r22)∴T2∝(r1+r22)3⇒T∝(r1+r22)3/2

A planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The time period of the planet is proportional to:

The correct option is C $(\frac{r_{1} + r_{2}}{2})^{3 / 2}$
According to Kepler's law,
$T^{2} \propto a^{3}$
Here, a $=$ semi-major axis $= (\frac{r_{1} + r_{2}}{2})$
$∴ T^{2} \propto (\frac{r_{1} + r_{2}}{2})^{3}$
$\Rightarrow T \propto (\frac{r_{1} + r_{2}}{2})^{3 / 2}$