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In this lesson, we will learn how to use Kepler's first, second, and third laws of planetary motion to determine the dynamics of elliptical orbits.

Q1:

The asteroid Eros has an elliptical orbit about the Sun, with a perihelion distance of 1.13 AU and aphelion distance of 1.78 AU. What is the period of its orbit?

Q2:

An asteroid has speed 15.5 km/s when it is located 2.00 AU from the sun. At its closest approach, it is 0.400 AU from the Sun. What is its speed at that point?

Q3:

A geosynchronous Earth satellite is one that has an orbital period of precisely one Earth day. A satellite in a geosynchronous orbit remains directly above a particular point on Earth’s surface throughout its orbit. What is the orbital radius of such a satellite if a day is considered as 8 6 4 × 1 0 3 s? Take the radius of Earth to be 6 3 7 0 km.

Q4:

If a planet with a mass that is 3.50 times that of Earth was orbiting the Sun at the same orbital radius at which Earth orbits the Sun, what would the planet’s orbital period be?

Q5:

A satellite in a geosynchronous circular orbit is 4 6 1 2 0 . 0 0 km from the centre of Earth. A small asteroid collides with the satellite, sending it into an elliptical orbit of apogee 4 3 0 0 0 . 0 0 km. What is the speed of the satellite at apogee? Assume that the satellite's angular momentum is conserved. Use 𝑚 = 5 . 9 7 2 1 9 × 1 0 𝐸 2 4 k g as Earth's mass.

Q6:

A satellite orbits Jupiter with an average orbital radius of 9 6 3 7 0 0 km and an orbital period of 3.269 days. Find the mass of Jupiter, considering a day as 8 6 4 . 0 × 1 0 3 s.

Q7:

The perihelion of Halley’s comet is 0.622 AU and the aphelion is 16.6 AU. The speed of Halley’s comet at the perihelion is 39 km/s. Find its speed at the aphelion. Use a value of 1 . 4 9 6 × 1 0 1 1 m for one AU.

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