In 1610 galileo made a telescope and used it to study the planet jupiter. he discovered four moons. one of them was ganymede. the mean radius of the orbit of ganymede around jupiter is 10.7 × 108m and the period of the orbit is 7.16 days. i) determine the mass of jupiter.

Explanation:

This problem can be solved by the Third Kepler’s Law of Planetary motion, which states:

“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.

In other words, this law stablishes a relation between the orbital period of a body (moon, planet, satellite) orbiting a greater body in space with the size of its orbit.

This Law is originally expressed as follows:

   (1)

Where;

 is the period of the orbit Ganymede describes around Jupiter

is the Gravitational Constant and its value is

is the mass of Jupiter  (the value we need to find)

 is the semimajor axis of the orbit Ganymede describes around Jupiter (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit)

If we want to find , we have to express equation (1) as written below and substitute all the values:

   (2)

   (3)

Finally:

  This is the mass of Jupiter

answer: b.

explanation:

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.