Respuesta :
The underlying force behind this change in velocity is the gravitational attraction between the Sun and the planet. In fact, the magnitude of the gravitational force is
[tex]G \frac{Mm}{r^2} [/tex]
where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance of the planet from the Sun
This force provides the centripetal force that keeps the planet in circular motion, so we can write:
[tex]G \frac{Mm}{r^2} =m \omega^2 r[/tex]
where the term on the right is the centripetal force, and [tex]\omega[/tex] is the angular speed of the planet. Simplifying the equation, we get
[tex]G \frac{M}{r^3}= \omega[/tex]
And from this equation we immediately see that, when the distance of the planet from the Sun (r) is small, the angular speed [tex]\omega[/tex] is larger and the planet travels faster; vice-versa, when the distance is large, the angular speed is smaller, and the planet travels slower.
[tex]G \frac{Mm}{r^2} [/tex]
where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance of the planet from the Sun
This force provides the centripetal force that keeps the planet in circular motion, so we can write:
[tex]G \frac{Mm}{r^2} =m \omega^2 r[/tex]
where the term on the right is the centripetal force, and [tex]\omega[/tex] is the angular speed of the planet. Simplifying the equation, we get
[tex]G \frac{M}{r^3}= \omega[/tex]
And from this equation we immediately see that, when the distance of the planet from the Sun (r) is small, the angular speed [tex]\omega[/tex] is larger and the planet travels faster; vice-versa, when the distance is large, the angular speed is smaller, and the planet travels slower.
The underlying force behind this change in velocity is the gravitational attraction between the Sun and the planet. In fact, the magnitude of the gravitational force is
where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance of the planet from the Sun
This force provides the centripetal force that keeps the planet in circular motion, so we can write:
where the term on the right is the centripetal force, and is the angular speed of the planet. Simplifying the equation, we get
And from this equation we immediately see that, when the distance of the planet from the Sun (r) is small, the angular speed is larger and the planet travels faster; vice-versa, when the distance is large, the angular speed is smaller, and the planet travels slower.
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