Regarding the radius in the orbital velocity

• I

Main Question or Discussion Point

Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity? If so, why? A body which moves passed a planet and starts orbiting it should have the same velocity it had before ,regarding the fact that it is orbiting a planet. Also, gravity isn’t really a force but the geometrical deformation of the fabric of space time. So really is like if you were riding your car in a tilted road so the car curves itself without the need of any forces acting upon it. The more the gravity the more the road is titled.

Related Other Physics Topics News on Phys.org
jtbell
Mentor
Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity?
Yes, because of conservation of energy. Gravitational potential energy is negative. Its magnitude increases with decreasing radius. The orbiting body's kinetic energy must increase in order to keep the total energy constant. You can observe this with bodies in elliptical orbits: they move fastest at the closest point to their central body, and slowest at the farthest point.

BvU
Homework Helper
2019 Award
Also, gravity isn’t really a force
Oh, isn't it ?

What is the gravitacional potencial energy? I’m not asking for the equations i just want to know what relation does gravity have with energy.

Yes, because of conservation of energy. Gravitational potential energy is negative. Its magnitude increases with decreasing radius. The orbiting body's kinetic energy must increase in order to keep the total energy constant. You can observe this with bodies in elliptical orbits: they move fastest at the closest point to their central body, and slowest at the farthest point.
What is the gravitacional potencial energy? I’m not asking for the equations i just want to know what relation does gravity have with energy.

osilmag
Gold Member
Also, gravity isn’t really a force but the geometrical deformation of the fabric of space time.
The force of gravity is defined as F=(Gm1m2)/r^2. You've probably seen it modeled as a fabric/grid.

osilmag
Gold Member
What is the gravitacional potencial energy? I’m not asking for the equations i just want to know what relation does gravity have with energy.
GPE is inversely related to the radius and directly proportional to mass and gravitational constant.

The force of gravity is defined as F=(Gm1m2)/r^2. You've probably seen it modeled as a fabric/grid.
Only according to Newton’s Law of Gravitation which is wrong. But we use his equations due to the fact that they are more simple to use and the solutions that they give us are very close to the real solution to gravity related problems. The accepted model of gravity is that of Einstein’s famous General Relativity. In which gravity is not a force but the presence of matter bending a fabric. Just like applying pressure to your bed and see how it sinks with your fist. Here she a link to an easy to see representation of gravity

russ_watters
Mentor
What is the gravitacional potencial energy? I’m not asking for the equations i just want to know what relation does gravity have with energy.
Energy is the potential to do work. Gravitational potential energy is therefore the ability for gravity to do work. In this case, applying a force to accelerate an object approaching another object.
Only according to Newton’s Law of Gravitation which is wrong.
Newton's Law of Gravitation is not "wrong" in a binary sense. It is highly accurate for most everyday purposes including the scenario you describe in this thread.

BvU
A.T.
The accepted model of gravity is that of Einstein’s famous General Relativity. In which gravity is not a force...
It's not an interaction force in GR, but can still be modeled as an inertial force, based on which potential energy can be defined.

...but the presence of matter bending a fabric. Just like applying pressure to your bed and see how it sinks with your fist. Here she a link to an easy to see representation of gravity
A very misleading analogy, as explained here:

See this for a more relevant analogy:

I’m not asking for the equations i just want to know what relation does gravity have with energy.
Equations is how relations are stated in physics.

Last edited:
LURCH
To understand gravitational Potential energy without using math, picture dropping a steel ball bearing on a plate of glass. Not a very heavy ball bearing, just a small one you could hold in your fingertips. If you drop it from a couple of inches, the glass vibrates, and you hear a sharp noise. Drop it from a couple of feet, and the noise will be much louder, and the bearing Will bounce. Drop it from 8 to 10 feet, and will break the glass. As you raise the bearing higher above the glass, you give it more potential to do work on the glass. When you release the bearing, that potential energy is converted into kinetic. As the bearing gets lower and lower, it’s speed increases. That is to say, it’s potential energy is converted into kinetic energy.

In orbital mechanics, this relationship works the same way. It is most easily seen in highly elliptical orbits. As the object “falls” closer to the center of gravity, it gains speed. After passing its closest point, it begins climbing again, and slowing down.

PeroK
Homework Helper
Gold Member
Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity? If so, why? A body which moves passed a planet and starts orbiting it should have the same velocity it had before ,regarding the fact that it is orbiting a planet. Also, gravity isn’t really a force but the geometrical deformation of the fabric of space time. So really is like if you were riding your car in a tilted road so the car curves itself without the need of any forces acting upon it. The more the gravity the more the road is titled.
To answer the why question directly. Because, the curvature of spacetime outside a spherical object is described by:

$ds^2 = -(1- \frac{2M}{r})dt^2 + (1- \frac{2M}{r})^{-1}dr^2 + r^2(d\theta^2 + \sin^2 \theta d\phi^2)$

Which leads to the "energy" equation of motion:

$E = \frac12(\frac{dr}{d\tau})^2 + V(r)$

Where $V(r)$ is the effective potential. This is the same equation as in Newtonian gravity, but in GR this potential has an additional term. For planetary orbits about the Sun, for example, this additional term is negligible, so we have a valid Newtonian approximation.

You may be thinking (from your rubber sheet or road analogies) that space itself has a defined shape and compels an object to move in a specific physical path. One problem with these analogies is that it is spacetime that is curved. So, one of the dimensions on your rubber sheet should be the time dimension, which is not so easy to visualise.

Because spacetime (space and time) are curved, the notion of "constant speed" is not so clear cut. We (as outside observers, using our system of coordinates - centred on the Sun, say) measure a change in coordinate velocity - that is not measurable as an acceleration by the orbiting body itself.