Which proportionality does Kepler’s third law describe?

Physics

2 answers:

Allisa [31]3 years ago

8 0

Size of a planet's orbit to sidereal period of the orbit

Blababa [14]3 years ago

3 0

Answer:

The third law of Kepler describes the proportionality of the orbital period and the semi-major axis of the orbit.

The square of the period of the orbit of a planet is proportional to the cube of the semi-major axis of the orbit.

The equation of the law is as follows:

$\frac{T^2}{a^3}=constant$

Where $T$ is the period and $a$ is the semi-major axis.

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a 75-kg refrigerator is located on the 70th floor of a skyscraper (300 meters above the ground) what is the potential energy of

kiruha [24]

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4 years ago

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Find the kinetic energy K of a satellite with mass m in a circular orbit with radius R. Express your answer in terms of m, M, G,

ratelena [41]

Answer:

$K=\frac{GmM}{2R}$

Explanation:

The kinetic energy is defined as:

$K=\frac{mv^2}{2}(1)$

Here, m is the object's mass and v its speed. In this case the speed of the satellite is the orbital speed, which is given by:

$v_{orb}=\sqrt\frac{GM}{R}(2)$

Here, G is the gravitational constant, M is the mass of the object that the satellite is orbiting and R is the radius of its circular orbit. Replacing (2) in (1):

$K=\frac{mv_{orb}^2}{2}\\K=\frac{m(\sqrt\frac{GM}{R})^2}{2}\\K=\frac{GmM}{2R}$