# Kepler's first law for any body

• B
I was just wondering, what if an object is placed in our solar system, will it revolve around the sun? If yes, will it have a centripetal acceleration too?

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Drakkith
Staff Emeritus
If an object is placed in the solar system with too small a tangential velocity relative to the Sun, then it will fall directly into it. Otherwise it will be put into either a closed or open orbit depending on its velocity.

If yes, will it have a centripetal acceleration too?
Certainly.

• Vishaaaal
Ibix
To add to @Drakkith's post, it might orbit or crash into a planet or moon, too. It depends where you put it and how fast it's moving in what direction.

• Vishaaaal
Janus
Staff Emeritus
Gold Member
Kepler's first law is based on the observation of the known planets of the time. Objects that were already in closed orbits around the Sun. It does not extend to every object that might be within the Sun's gravitational influence. The ellipse is one solution for the path for such an object, other solutions are a parabola or hyperbola. (and circle, which is really just a special case of ellipse.)
Which of the paths the object follows depends on its velocity and distance from the Sun at at given point. Parabolas or Hyperbolas will be followed by objects that are moving too fast to be in a closed orbit. (the parabola actually is the "dividing line" between a elliptical and hyperbolic path. If you pick any distance from the Sun, there is a velocity at which the object would be traveling in a parabola, Anything slower than this would result in a closed elliptical orbit and anything faster result in a hyperbola.
Even if the velocity is such that you have an ellipse is not a guarantee that you will end up with a stable orbit. This will depend on the "eccentricity" or flatness of the orbit. If the object at our given distance from the Sun is moving too slow our its direction of movement is pointed to much towards the Sun, the orbit will be so eccentric that it orbit will take it into the surface of the Sun. So what we end up with is a range of possible solutions that end up giving us a stable orbit, and anything out side this range does not.

As far as centripetal acceleration goes, all objects within the Sun' gravitational influence are subject to it, as it is the Sun's gravity that produces it.

• Vishaaaal
If an object is placed in the solar system with too small a tangential velocity relative to the Sun, then it will fall directly into it. Otherwise it will be put into either a closed or open orbit depending on its velocity.
Thanks mate. Answered my question in the best possible way. So....the orbit does not depend upon its mass right?

Drakkith
Staff Emeritus
Thanks mate. Answered my question in the best possible way. So....the orbit does not depend upon its mass right?
As long as the mass of the object is significantly smaller than that of the Sun, then you can mostly ignore it.

• Vishaaaal
Kepler's first law is based on the observation of the known planets of the time. Objects that were already in closed orbits around the Sun. It does not extend to every object that might be within the Sun's gravitational influence. The ellipse is one solution for the path for such an object, other solutions are a parabola or hyperbola. (and circle, which is really just a special case of ellipse.)
Which of the paths the object follows depends on its velocity and distance from the Sun at at given point. Parabolas or Hyperbolas will be followed by objects that are moving too fast to be in a closed orbit. (the parabola actually is the "dividing line" between a elliptical and hyperbolic path. If you pick any distance from the Sun, there is a velocity at which the object would be traveling in a parabola, Anything slower than this would result in a closed elliptical orbit and anything faster result in a hyperbola.
Even if the velocity is such that you have an ellipse is not a guarantee that you will end up with a stable orbit. This will depend on the "eccentricity" or flatness of the orbit. If the object at our given distance from the Sun is moving too slow our its direction of movement is pointed to much towards the Sun, the orbit will be so eccentric that it orbit will take it into the surface of the Sun. So what we end up with is a range of possible solutions that end up giving us a stable orbit, and anything out side this range does not.

As far as centripetal acceleration goes, all objects within the Sun' gravitational influence are subject to it, as it is the Sun's gravity that produces it.
Can you provide an example to me? Its just that I began taking Physics seriously this year and the laws don't seem too realistic to me.

As long as the mass of the object is significantly smaller than that of the Sun, then you can mostly ignore it.
All of my doubts are cleared...thanks pal :)

Ibix
Can you provide an example to me? Its just that I began taking Physics seriously this year and the laws don't seem too realistic to me.
What, Kepler's laws, or physics in general?

Kepler's laws are observational rules of thumb, basically. He says "these things are true of the observed movements of the planets" without providing any explanation. Newton provided the theory a few years later. Ellipses, parabolae and hyperbolae are the solutions to differential equations describing the motion of a free-falling body in a force field with ##1/r^2## behaviour, like gravity.

The reality isn't quite like that. Some solutions are curves that intersect the star. Strictly, the paths are only correct for massless bodies because they assume that the Sun doesn't move under the gravity of the planets (which is very close to true given the mass ratio, but not quite). Also, the planets' gravitational fields affect each other so their orbits aren't as simple as ellipses. Finally, Newton's theory of gravity is slightly wrong, and provides predictions that aren't quite right. That General Relativity accounted for the (tiny) anomalous precession of Mercury's orbit was a major boost to its credibility.

• Vishaaaal
What, Kepler's laws, or physics in general?

Kepler's laws are observational rules of thumb, basically. He says "these things are true of the observed movements of the planets" without providing any explanation. Newton provided the theory a few years later. Ellipses, parabolae and hyperbolae are the solutions to differential equations describing the motion of a free-falling body in a force field with ##1/r^2## behaviour, like gravity.

The reality isn't quite like that. Some solutions are curves that intersect the star. Strictly, the paths are only correct for massless bodies because they assume that the Sun doesn't move under the gravity of the planets (which is very close to true given the mass ratio, but not quite). Also, the planets' gravitational fields affect each other so their orbits aren't as simple as ellipses. Finally, Newton's theory of gravity is slightly wrong, and provides predictions that aren't quite right. That General Relativity accounted for the (tiny) anomalous precession of Mercury's orbit was a major boost to its credibility.
Kinda got it (y)