- #1
physicallove
- 3
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why does mercury move with such velocity while pluto is much slower?
Dickfore said:The centripetal acceleration is:
[tex]
a = \frac{v^{2}}{r}
[/tex]
If this acceleration is provided by a gravitational force $F(r)$ from the Sun, that somehow varies with distance, then:
[tex]
F(r) = m a
[/tex]
From here. by knowing how the force varies with distance, we can find how the velocity varies with distance:
[tex]
v(r) = \sqrt{\frac{r F(r)}{m}}
[/tex]
The velocity will not depend on distance iff:
[tex]
F(r) = O(\frac{1}{r})
[/tex]
If the gravitational force falls off with distance faster than this, then the orbital velocity of more distant bodies should decrease. On the other hand, if it falls off more slowly, then it will increase.
The main factors that affect the planetary motion of Mercury and Pluto are gravity, the Sun's gravitational pull, and the planets' orbital speeds and distances from the Sun.
Einstein's theory of relativity helps to explain the discrepancies in the orbit of Mercury by taking into account the effects of gravity on spacetime. It also helps to understand the irregular orbit of Pluto, which is greatly influenced by the gravity of Neptune.
Mercury orbits the Sun at a much closer distance compared to Pluto, resulting in a shorter orbital period and faster speed. Pluto, on the other hand, has a highly elliptical orbit and is much farther from the Sun, resulting in a longer orbital period and slower speed.
Advancements in technology, such as telescopes and space probes, have allowed us to gather more precise data and observations of these planets, leading to a better understanding of their orbital patterns and characteristics.
Yes, the planetary motion of Mercury and Pluto can change over time due to various factors such as gravitational interactions with other planets, impacts from asteroids or comets, and the gradual shifting of the planets' orbits due to the influence of the Sun's gravity.