Does the speed of a falling object depend on its mass? What about the speed of a satellite in orbit?

Question

Does the speed of a falling object depend on its mass? What about the speed of a satellite in orbit?

Answer 1

Two objects dropped from the same height fall at the same speed no matter how big or small the other one is.

Answer 2

The acceleration due to the Earth's gravity is 32 feet per second per second. If gravity is the only force, then everything falls at this speed. However, there are usually other forces than gravity, most often the resistance of the air. The resistance of the air, often called wind resistance, depends on the shape of the object and also its weight, thus a falling object does depend on its mass, since mass would be a factor in determing wind resistance. The speed of a satellite in orbit depends on two things, the height of the orbit and the attraction of gravity. The mass of the object has no effect on speed.

Answer 3

The classic text book answer is NO - the famous experiment where a cannon ball and a small ball were dropped off the leaning tower of pizza, showed that both hit the ground at the same time - if mass or weight had anything to do with it, then the speeds would change equal to the difference in mass, or 7 times.

The actual answer is YES - turn the situation upside down. Since gravity affects things based on the amount of mass, then the small ball would pull the earth down 1/7th of the force of the larger cannon ball. However, since the earth is such a large object, billions of times heavier than either object, the difference is almost undetectable on common land based experiments,

In space, where there is no atmosphere, the situation is different, and tiny changes in mass will affect the " FALLING " of the object as it falls around the earth. To compensate you either have to move the object to a higher or lower orbit, or increase or decrease the speed to maintain a stable orbit ( path of falling to earth )

Answer 4

The speed of a falling object depends on its mass only with regard to air resistance, which affects the terminal velocity of objects. There are other factors, such as the shape of the object, which also play a part in this. The speed of a satellite in orbit does not depend on its mass, because there is no air resistance once you are outside of the atmosphere.

To understand why the speed does not depend on mass, we need to understand Newton's laws. Newton's law of Gravity states that the force of gravity between two objects is equal to a constant (we'll call it G) times the mass of the first object times the mass of the second object, divided by the square of the distance between the objects. Newton's Second Law of Motion states that force = mass times acceleration. So:

Law of Gravity:
F = G * m1 * m2 / d^2

2nd Law of Motion:
F = ma

So to find the force of gravity on an object from the earth, we can say m1 = mass of object, m2 = mass of earth:

F = G * m1 * m2/d^2 = m1a

Solving for a, we see that the mass of the object cancels out on both sides, and we have:

a = G * m2/d^2

Therefore the acceleration given to an object by the earth does not depend on its mass. The heavier the object the more force it gets because of gravity, but it also takes more force to move a heavier object, and these two differences exactly cancel each other out.

Answer 5

The velocity of a falling object in a vaccuum does not depend on its mass. Galilaeo demonstrated this hundreds of years ago by putting objects of different mass in vaccuum cylinders and dropping them off a building. If you look at the equation for the acceleration of an object due to gravity it is 1/2 at^2 where a is the acceleration due to gravity which is about 10m/s/s. Since mass is not in this equation, you can conculde that mass has no effect. If you take the real world, of course everything changes. Then the aerodynamics of the falling objects matter and if the aerodynamics are affected by mass due to some type of deformation, the speed will be affected.

Answer 6

Falling Bodies: Galileo Galilei figured that out in 1581. (He was 17 years old. Sharp kid.)
Speed of a satellite :
the a speed of a satellite in low earth orbit is somewhere around 17,125 MPH. See the reference.
Lets look at a geosynchronous satellite. It sits approximately 26,200 miles from the center of the earth. In order to stay directly above the same spot on earth, the satellite must circle the earth once a day. Do the math.
Radius of the circle: Two times the radius times pi: (2 pi r)
2 x 26,200 X 3.14 = 164536 miles
That radius, divided by the hours in a day (24)
164,536 / 24 = 6856 miles per hour.
That's funny, I thought it would be faster.

Hope this helps.

Answer 7

You need to state your assumptions.

Any two objects will accelerate at exactly the same rate towards the surface of a planet as long as:

1. Neither object is similar in mass to or more massive than the planet itself.

2. There is no atmosphere to provide an opposing force.

On the question of satellites in orbit, as long as both satellites are relatively small in comparison to the planet and both satellites are in an orbit with similar eccentricity and semi-major axis length, then they will orbit the planet at the same rate. If one satellite is in a much higher or lower orbit, it will move more slowly or more quickly than the other satellite.

Higher orbits move more slowly and lower orbits move more quickly.

Answer 8

In a vacuum, that is, the only force acting on any mass being the force do to gravity, an object accelerates at the same speed as any other object, reguardless of mass. I'll explain:

For an object to have weight (a force that varies based on mass, UNLIKE the value for the acceleration due to gravity on any one mass), it must have a normal force acting against that weight equal to the value of the object's weight itself perpendicular to the suface upon which the object rests. Think about it this way:

Imagine yourself standing on the ground, on planet earth. Gravity continuously acts upon your mass in an effort to accelerate you to the center of the planet, but why do you stand as if nothing's happening? Simple: your weight (a force which always acts down) is beign opposed by what is called, again, the normal force, (which always acts against weight, and is equal to weight at all times). The normal force is the force the ground has upon you so that you don't "fall through it." If it so happened that you did "fall through the ground" like a paper weight would "fall through a sheet of paper" in the air, your weight simply exceeds the normal force meant to keep the mass from falling through.

Now, back to the question at hand. A falling object doesn't have mass because there is no surface upon which a normal force to act upward upon. No normal force means no weight. As you can see, this statement would go for ANY mass in free-fall, reguardless OF its mass. Mass in the case of freely falling objects does not matter in the least.

The speed of a satellite in orbit around a planet (whether it be an artificial one like ones used in broacadsting signals around the world or natural ones like our Moon) depends mainly upon the quantitative value for the gravitational pull of both the earth and the moon. The moon's mass gives it a certain quantity for as to how much gravitational pull it would exert on another mass, as is the same true for Earth. The speed of the moon is defined as the speed at which the moon must travel in order to avoid "falling into the Earth" completely. This speed must equal the gravitational pull of the Earth (which is dependent upon its mass); if too small, it'll fall straight into and collide with the Earth; if too great the speed, it'll never remain captured within the pull of Earth's graviation.

Answer 9

In air, the speed of a falling object will depend on its mass, density, aerodynamic shape, air density, and probably a few other things. In a vacuum, it depends only on g, the acceleration due to gravity - normally 9.8 m/s^2.

The speed of a satellite in orbit depends only on the height and shape of its orbit.

Answer 10

these are somewhat entirely different questions. :p

1. according to Newtonian physics, no, the mass of a falling object does not affect its rate of fall, but rather what affects it is the gravity of the pulling body. but according to Einsteinian physics, mass is indeed energy, and the greater the mass of a body, the stronger its pull of [gravity]. this is also considered in Newtonian physics, but what's often overlooked is that aside from the pulling body (i.e. Earth), the falling body is also exerting a pull on the pulling body (i.e. when you fall, you're actually "pulling} yourself to the ground, aside from the ground pulling you). in most day-to-day cases, this effect is so minute that it's completely negligible though. :p

2. the speed of a satellite in orbit, following the above explanation has to be at least a bit hampered by the gravity of the body it is orbiting. but the speed of a satellite is not supposed to be related only to its mass, but rather, the speed of the planet's rotation and its distance from the planet (i.e. the Earth). a satellite moves at just the right speed to not fall into the planet AND not hurtle into space. technically speaking, a satellite moves in a straight line, but the gravity of its orbited body makes it go into a circular path, and if the speed if just right, it won't fall into it, nor escape its pull.