Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_1$ exerts on $m_2$ is
$\frac{{{m_1}{m_2}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{{m_1}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{{m_2}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{G({m_1} + {m_2})}}{{{{({r_1} + {r_2})}^2}}}$
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac {a}{2}$ distance from the centre, will be
A geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-
A satellite of mass $m$ is in a circular orbit of radius $2R_E$ about the earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ is the mass and radius of the earth respectively)
On a hypothetical planet satellite can only revolve in quantized energy level i.e. magnitude of energy of a satellite is integer multiple of a fixed energy. If two successive orbit have radius $R$ and $\frac{3R}{2}$ what could be maximum radius of satellite
In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth, the work done is