Kepler's discovered that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit, that is called Kepler's third law of planet motion and can be expressed as:

$T=\frac{2\pi a^{\frac{3}{2}}}{\sqrt{GM}}$ (1)

with T the orbital period, M the mass of the sun, G the Cavendish constant and a the semi major axis of the elliptical orbit of the planet. By (1) we can see that orbital period is independent of the mass of the planet and depends of the semi major axis, rearranging (1):

$\frac{T}{a^{\frac{3}{2}}}=\frac{2\pi}{\sqrt{GM}}$

$\frac{T^{2}}{a^{3}}=(\frac{2\pi }{\sqrt{GM}})^2$ (2)

Because in the right side of the equation (2) we have only constant quantities, that implies the ratio $\frac{T^{2}}{a^{3}}$ is constant for all the planets orbiting the same sun, so we can said that:

$\frac{T_{A}^{2}}{a_{A}^{3}}=\frac{T_{B}^{2}}{a_{B}^{3}}$

$\frac{T_{B}^{2}}{T_{A}^{2}}=\frac{a_{B}^{3}}{a_{A}^{3}}$

$\frac{T_{B}}{T_{A}}=\sqrt{\frac{a_{B}^{3}}{a_{A}^{3}}}=\sqrt{\frac{(2a_{A})^{3}}{a_{A}^{3}}}$

$\frac{T_{B}}{T_{A}}=\sqrt{\frac{2^3}{1}}=2.83$

6 0

2 years ago

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A steel ball and a piece of clay have equal mass. They are dropped from the same height on a horizontal steel platform. The ball

emmasim [6.3K]

Answer: The ball (option A)

Explanation: change in momentum is defined by the formulae m(v - u) where m = mass of object, v = final velocity and u = initial velocity.

For the ball, it hits the ground and bounces back with the same speed, that's final velocity equals initials (v = - u)

Change in momentum = m( -u- u) = m(-2u) = m(-2u) = -2mu

For the clay, it final velocity is zero since it sticks to the floor, hence (v =0)

m(v - u) = m(0 - u) = - mu.

-2mu (change in momentum from the ball) is greater than - mu ( change in momentum of clay)

6 0

2 years ago

A car has an acceleration of -5 m/s^2. Describe the car’s motion

AlladinOne [14]

Explanation:

because the acceleration is negative, this indicates a deceleration (or slowing down) . Hence we can say that:

The car is decelerating (slowing down), i.e its velocity is decreasing, at a constant rate of 5m/s².

7 0

3 years ago

What is the measure of a change in an object’s velocity?

tiny-mole [99]

It's a measure of the acceleration

6 0

2 years ago