Orbits

What does Kepler's second law state about the shape of planetary orbits?

A line connecting a planet to the Sun sweeps out equal areas in equal time.

What does Kepler's first law state about the shape of planetary orbits?

Planets move in elliptical orbits with the Sun at one focus of the ellipse.

What is the relationship described in Kepler's third law?

The square of a planet's orbital period (T²) is proportional to the cube of its semi-major axis (r³).

What is Newton's Law of Universal Gravitation?

F = G (M1 * M2) / r², where F is the gravitational force, G is the gravitational constant, M1 and M2 are the masses of two objects, and r is the distance between their centers.

How does the distance affect the gravitational force between two masses according to Newton's law?

The gravitational force is proportional to 1/r²; if the distances double, the force decreases by a factor of four.

What role does gravity play in maintaining planetary orbits?

The Sun's gravity provides the necessary centripetal force for planets to stay in orbit.

How is the mass of a central object calculated using orbital data?

Using Kepler's third law: M = 4π²r³ / GT², where T is the orbital period and r is the distance from the star.

What is the dark matter hypothesis in relation to spiral galaxies?

The observed flat rotation curves of stars suggest extra unseen mass, or dark matter, that provides additional gravitational pull.

What is the role of the Higgs boson in relation to mass?

The Higgs boson is responsible for giving mass to fundamental particles.

What is the formula for the centre of mass of two orbiting bodies?

R = (M1 * d1 + M2 * d2) / (M1 + M2), where d1 and d2 are distances from the centre of mass.