The mass of the planets?

[skeptic1]

The mass of the planets is calculated by taking the centripetal force (mass of planets times its velocity squared divided by the distance to the sun squared) to gravitational force (the mass of the planet times the mass of the sun divided by the distance between them squared) between the sun and planet. To solve the equation you multiply both sides of the equation by the distance between them squared divided by the mass of the planet. The result is the mass of the sun is equal to the velocity of the planet squared. This is high school algebra. You cannot find the mass of objects using the force of gravity. The rate an object falls or the velocity of an object in orbit have nothing to do with their mass. There is no force of gravity or force associated with mass.

[imatfaal]

The mass of the planets is calculated by taking the centripetal force (mass of planets times its velocity squared divided by the distance to the sun squared) to gravitational force (the mass of the planet times the mass of the sun divided by the distance between them squared) between the sun and planet. To solve the equation you multiply both sides of the equation by the distance between them squared divided by the mass of the planet. The result is the mass of the sun is equal to the velocity of the planet squared. This is high school algebra. You cannot find the mass of objects using the force of gravity. The rate an object falls or the velocity of an object in orbit have nothing to do with their mass. There is no force of gravity or force associated with mass.

 

"There is no force of gravity or force associated with mass."

 

[latex]F_{grav} = -\frac{Gm_1m_2}{r^2}[/latex]

"You cannot find the mass of objects using the force of gravity." How do you think bathroom scales work?

[Greg H.]

The mass of the planets is calculated by taking the centripetal force (mass of planets times its velocity squared divided by the distance to the sun squared) to gravitational force (the mass of the planet times the mass of the sun divided by the distance between them squared) between the sun and planet. To solve the equation you multiply both sides of the equation by the distance between them squared divided by the mass of the planet. The result is the mass of the sun is equal to the velocity of the planet squared. This is high school algebra. You cannot find the mass of objects using the force of gravity. The rate an object falls or the velocity of an object in orbit have nothing to do with their mass. There is no force of gravity or force associated with mass.

 

The universe disagrees with you. Guess which one of two is wrong?

[Janus]

The mass of the planets is calculated by taking the centripetal force (mass of planets times its velocity squared divided by the distance to the sun squared) to gravitational force (the mass of the planet times the mass of the sun divided by the distance between them squared) between the sun and planet. To solve the equation you multiply both sides of the equation by the distance between them squared divided by the mass of the planet. The result is the mass of the sun is equal to the velocity of the planet squared. This is high school algebra. You cannot find the mass of objects using the force of gravity. The rate an object falls or the velocity of an object in orbit have nothing to do with their mass. There is no force of gravity or force associated with mass.

The mass of the planets are notcalculated from their orbits around the Sun but from the orbits of their moons. In essence, you take the equation:

 

[math]T^2 = \frac{4 \pi^2 r}{GM}[/math]

 

Where T is the period of the moon's orbit and r is the radius of its orbit, and solve for M the mass of the planet.

 

As long as the mass of the moon is very small as compared to the planet, you will get an accurate enough answer.

 

With Mercury and Venus, which have no natural moons, we could only estimate mass from their size until we visted them with probes. The trajectories of these probes as they passed the planets gave us more accurate measurements of their masses.

 

However, I must point out the caveat I mentioned earlier: the moon needs to have a small mass compared to the planet. This is because your statement of the mass of an object having no effect on its orbit is incorrect in the strictest sense. This is beause the object doesn't really orbit the center of the larger object. Instead both orbit the barycenter, or common center of mass for both.

 

When one object is much more less massive than the other, this barycenter is very close to the center of the larger body, and in most cases we can ignore this difference. However, as the mass of the smaller body increases, the barycenter moves closer and closer to the smaller object. This changes both the orbital velocity and period of the orbit. (the radius of the orbit decreases, however the distance between the bodies, and thus the gravitational force holding it in orbit does not.)

 

In this case, the period of the orbit will give the total mass of moon and planet, while the relative motion around the barycenter give the relative masses of moon and planet.

[J.C.MacSwell]

 

"There is no force of gravity or force associated with mass."

 

[latex]F_{grav} = -\frac{Gm_1m_2}{r^2}[/latex]

"You cannot find the mass of objects using the force of gravity." How do you think bathroom scales work?

Not very well...while in orbit/freefall...

[Enthalpy]

the centripetal force (mass of planets times its velocity squared divided by the distance to the sun squared) to gravitational force (the mass of the planet times the mass of the sun divided by the distance between them squared) between the sun and planet.

Centrifugal, distance squared, mass of the planet times the mass of the sun times G...

[swansont]

Centrifugal, distance squared, mass of the planet times the mass of the sun times G...

 

The gravitational force on an orbiting object is a centripetal one.

[Enthalpy]

And the stated m*V²/R is centrifugal, which compensates the centripetal gravitation force.