Let's discuss a problem where we find out the time periods of revolution of two stars.
The problem: Time Periods of Revolution of Two Stars
The masses of two stars are (m_1) and (m_2) and their separation is (l). Determine the period (T) of their revolution in circular orbits about a common centre.
Since the system is closed, the stars will rotate about their common centre of mass in concentric circles. The equation of motion for the stars will have the form $$ m_1\omega_1^2l_1=F$$ and $$ m_2\omega_2^2l_2=F......(1)$$
Here (\omega_1) and (\omega_2) are the angular velocities of rotation of the stars, (l_1) and (l_2) are the radii of their orbits, (F) is the force of interaction between the stars, equal to (\frac{Gm_1m_2}{l^2}) where (l) is the seperation between the stars and (G) is the gravitational constant.
By the definition of centre of mass,
$$ m_1l_1=m_2l_2$$
$$l_1+l_2=l...... (2)$$
Solving equations 1 and 2 together, we get
$$ \omega_1=\omega_2=\sqrt{\frac{G(m_1+m_2)}{l^3}}$$
The required period of revolution of these stars is $$ T=2\pi l\sqrt{\frac{l}{G(m_1+m_2)}}$$
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
