Does relative mass equal weight? Does weight times spin make gravity?

Question

I only ask because Einstien said that planets are heavy and make dents in space time etc, and that rest energy = relative mass times light speed in a vacuum squared.
Yet if relative mass does not mean weight (I think that weight is also affected by density) then wouldn't the theory of relativity have to take account of this?
I read for example that if you took Saturn and dropped it in a bath it would float.
Does that mean it is light relative to its size? Does that mean it is not heavy? Does that mean it does not make a dent in space time relative to its size because it is not heavy?
Is it weight or size that makes a dent in space time?
Does rest energy = mass and density and spin and movement and relation to other bodies whilst in a stationary orbit?

Answer 1

You are mixing up several different concepts here: mass, weight, density. Weight is a force, not a mass. Weight is the effect of gravity on a mass and depends on the strength of the gravitational field as well as the mass. Rest mass and relativistic mass are both masses and both are affected by gravity. Light has zero rest mass, but it has relativistic mass from its energy. Therefore light is affected by gravity. Density is just mass divided by volume. Something may be very massive, like a planet, but if it is also very large, its density could be low. Whether something floats on water depends on its density relative to water, not its mass. To say that Saturn would float on water is only saying that its density is less than water. The "dent" in spacetime depends on mass only when outside the massive body itself. The same "dent" is produced even if all the mass is concentrated in a small point, as long as we are measuring the dent outside the mass itself. In this case, size doesn't matter. I don't understand your last question.

Answer 2

Mass is the amount of substance.
Weight is the force acted on a mass by another mass.
Density is the amount of mass in a unit volume of the mass. It has nothing to do with weight.
Saturn would float in a (very) big bath of water because a volume of water the size of Saturn would have more mass and, so, be more dense. Water is more dense than Saturn.
Saturn is very 'heavy' if by 'heavy' is meant contains a lot of mass.
It does make a dent in space-time. It has many satellites that are affected by this dent. Also the rings would not exist if it didn't make a dent.
A satellite can orbit a planet in such a way as to revolve around the planet in the same time that the planet rotates on its axis. Provided that the satellite is in the planet's equatorial plane, it will appear to stay above the same spot on the surface of the planet. This is a stationary orbit. There is only one distance from the planet's centre that a stationary orbit is possible. This distance depends only on the mass of the planet.

Answer 3

Keeping it simple the answer to your question is that for example, a one pound weight will weigh 1 pound here on earth. On the moon it will weigh less. The reason is that on the moon it has less weight as the gravity is lower and does not pull down on the 1 pound weight as much. By pulling down on the mass just think that anything that is dropped from a height, will fall to the ground only. This is the effect of gravity.
However the 1 pound weight has not changed it's mass. It is no larger or no smaller. On a larger planet therefore the weight will be far greater but the mass will be the same.

Answer 4

Gravity is the result of the curvature of space. Take a bowling ball and place it at the center of your bed. When smaller balls are placed on the bed they will tend to move towards the bowling ball, because of the inclination towards the center.