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Gravitational Fields and Kepler's Laws of Orbital Motion for IB Physics

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An aircraft is flying at an altitude of 10.0 km above sea level. The average radius of Earth is 6370 km. Calculate the ratio:

0.997

Determine the height above sea level at which the gravitational field strength is reduced to 99% of its value at sea level.

32 km

Two asteroids X and Y can be modelled as uniform spheres of the same density. The radius of asteroid X is twice that of asteroid Y. What is the ratio:

A satellite orbits Earth in an elliptical orbit in the direction represented by the arrow. At which position is the kinetic energy of the satellite increasing?

Satellites X and Y move in circular orbits around a planet. The orbital period of satellite X is 16 days. The orbital radius of satellite Y is 1/4 of the orbital radius of satellite X. Calculate the orbital period of satellite Y.

2.0 days

An asteroid moves around the Sun in a circular orbit. The following data are given: Orbital period of the asteroid = 3.6 years; Sun–Earth distance = 1.5 × 10^11 m Calculate, in m, the radius of the asteroid’s orbit.

3.5 × 10^11 m

Phobos and Deimos are two moons of Mars that move in approximately circular orbits. The radius of Phobos’ orbit is 9.4 × 10^6 m and its orbital period is 7.7 hours. Calculate the mass of Mars.

6.4 × 10^23 kg

Phobos and Deimos are two moons of Mars that move in approximately circular orbits. The radius of Phobos’ orbit is 9.4 × 10^6 m and its orbital period is 7.7 h. Deimos's orbital period is 30 hours. Calculate the radius of Deimos’ orbit.

2.3 × 10^7 m

A satellite is placed in a circular orbit 100 km above the surface of the Moon. Calculate the orbital period of the satellite. Mass of the Moon = 7.35 × 10^22 kg; Radius of the Moon = 1.74 × 10^6 m

7.08 × 10^3 s (approximately 2 hours)