\(T\) is the time period of revolution of a planet revolving around the sun in an orbit of mean radius \(R\). Identify the incorrect graph.

1.		2.
3.		4.

A planet revolving in elliptical orbit has:

Choose the correct answer from the options given below:

A planet of mass \(m\) is moving around a star of mass \(M\) and radius \(R\) in a circular orbit of radius \(r.\) The star abruptly shrinks to half its radius without any loss of mass. What change will be there in the orbit of the planet?

The law of gravitation states that the gravitational force between two bodies of mass \(m_1\) $\mathrm{and}$ \(m_2\) is given by:
\(F=\dfrac{Gm_1m_2}{r^2}\)
$\mathrm{}$\(G\) (gravitational constant) \(=7\times 10^{-11}~\text{N-m}^2\text{kg}^{-2}\)$\mathrm{.}$
\(r\) (distance between the two bodies) in the case of the Earth and Moon $\mathrm{}$\(=4\times 10^8~\text{m}\)
\(m_1~(\text{Earth})=6\times 10^{24}~\text{kg}\)
\(m_2~(\text{Moon})=7\times 10^{22}~\text{kg}\)
${\mathrm{}}_{}$What is the gravitational force between the Earth and the Moon?
1. \(1.8375 \times 10^{19}~\text{N}\)
2. \(1.8375 \times 10^{20}~\text{N}\)
3. \(1.8375 \times 10^{25}~\text{N}\)
4. \(1.8375 \times 10^{26}~\text{N}\)

An artificial satellite revolves around a planet for which gravitational force \((F)\) varies with the distance \(r\) from its centre as \(F \propto r^{2}.\) If \(v_0\) is its orbital speed, then: