1. The acceleration due to gravity on the earth depends upon
Answers
Answer:
The gravitational acceleration depends on only the mass of the gravitating object M and the distance d from it.
Answer:
Galileo found that the acceleration due to gravity (called ``g'') depends only on the mass of the gravitating object and the distance from it. It does not depend on the mass of the object being pulled. In the absence of air drag, a huge boulder will fall at the same rate as a small marble dropped from the same height as the boulder. A tiny satellite at the same distance from the Sun as Jupiter's orbit from the Sun feels the same acceleration from the Sun as the large planet Jupiter does from the Sun. (The satellite and Jupiter will also, therefore, have the same orbital period around the Sun.) How is this possible? Most people would agree with Aristotle that the bigger object should fall faster than the smaller object, but experiments show they would be wrong. One particularly nice illustration of this was done on the Moon by Commander David Scott of Apollo 15 when he dropped a hammer and a feather from the same height. See the video on the Apollo 15 Hammer-Feather Drop page.
A boulder falling toward the Earth is pulled by a stronger gravity force than the marble, since the boulder's mass is greater than the marble, but the boulder also has greater resistance to a change in its motion because of its larger mass. The effects cancel each other out, so the boulder accelerates at the same rate as the marble. The same line of reasoning explains the equal acceleration experienced by Jupiter and the satellite.
You can use Newton's second law of motion F = m × a (which relates the acceleration, a, felt by a object with mass m when acted on by a force F) to derive the acceleration due to gravity (here replace a with g) from a massive object:
The force of gravity =
(G M m)
d2
= m g
so
g =
(G M)
d2
.
The gravitational acceleration depends on only the mass of the gravitating object M and the distance d from it. Notice that the mass of the falling object m has been cancelled out. This explains why astronauts orbiting the Earth feel ``weightless''. In orbit they are continually ``falling'' toward the Earth because of gravity (the Earth's surface curves away from them at the same rate they are moving forward). If Jane Astronaut drops a pen in the space shuttle, it accelerates toward the Earth, but she accelerates by the same amount so the pen remains at the same position relative to her. In fact the entire shuttle and its contents are accelerating toward the Earth at the same rate, so Jane and her companions ``float'' around inside! This is because all of them are at very nearly the same distance from the Earth.The acceleration decreases with the SQUARE of the distance (inverse square law). To compare gravity accelerations due to the same object at different distances, you use the gravity acceleration g at distance A = (the gravity acceleration g at distance B) × (distance B / distance A)2. Notice which distance is in the top of the fraction. An example of using the inverse square law is given in the ``How do you do that?'' box below.