Using Kepler's third law and his own second law, Newton found that the *amount*
of the attractive
force, called gravity, between a planet and Sun a distance *d* apart is Force
= k_{p} × (planet mass) /
(d)^{2}, where k_{p} is a number that is the
same for all the planets. In the same way he found that the *amount* of the
gravity between the Sun and a planet is Force = k_{s} × (Sun mass) /
(d)^{2}. Using
his third law of motion, Newton reasoned that these forces must be the same (but
acting in the opposite directions). He derived his **Law of Gravity**: the
force of gravity = *G* × (mass #1) × (mass #2) /
(distance between them)^{2} and this force is directed toward
each object, so it is always attractive. The term *G* is a universal constant
of nature. If you use the units of
kilograms (kg) for mass and meters (m) for distance, *G* = 6.672 × 10^{-11}
m^{3} /(kg sec^{2}). If you need a refresher on exponents, square
& cube roots, and scientific
notation, then please study the math review appendix.

Spherically
symmetric objects (eg., planets, stars, moons, etc.) behave as if all of their mass
is concentrated at their centers. So when you use Newton's Law of Gravity, you
measure the distance between the *centers* of the objects.

In a bold, revolutionary step, Newton stated that his gravity law worked for
*any* two objects with mass---it applies for any motions on the Earth, as well
as, any motions in space. He unified celestial and terrestrial physics and completed
the process started by Copernicus of removing the Earth from a unique position or
situation in the universe. His law of gravity also explained Kepler's 1st and
2nd laws.

The UNL Astronomy Education program's **Planetary
Orbit Simulator** shows you how a planet's velocity and accelearation
relate to its orbits and Kepler's laws (link will
appear in a new window).

Because the masses are in the top of the fraction, more mass creates more gravity force.
This also means that more massive objects produce greater accelerations
than less massive objects. Since distance is in the bottom of the fraction, gravity has
an *inverse* relation with distance: as distance *increases*, gravity
*decreases*. However, gravity never goes to zero---it has an infinite range (in
this respect it is like the electrical and magnetic forces). Stars feel the gravity
from other stars, galaxies feel gravity from other galaxies, galaxy clusters feel
gravity from other galaxies, etc. The always attractive gravity can act over the
largest distances in the universe.

There is no way to
get rid of the *force* of gravity. If you want to prevent a body from
producing a
gravitational *acceleration* on
an object, you need to use a second body, with the same amount of gravity pull
as the first body, in a way that its gravity pulling on the object is in the
opposite direction. The resulting *accelerations* due to the forces
from the two bodies will cancel each other out.

- What basic fundamental assumption did Newton make about the laws of nature on the Earth and in space?
- Why is gravity often the most important force in astronomical interactions?
- What things does gravity depend on?
- How does gravity vary with distance between objects and with respect to what do you measure the distances?
- What would happen to the orbit of Io (one of Jupiter's moons) if all of the Hydrogen and Helium in Jupiter were converted to Silicon and Oxygen? Explain your answer.
- What would happen to the Earth's orbit if the Sun suddenly turned into a black hole (of the same mass)? Why?
- How would
*anti*matter respond to gravity? (Hint: antimatter has mass just like ordinary matter.) - What important laws of planet motion can be derived from Newton's law of gravity?
- Use Newton's laws of motion and gravity to answer the two questions given in the figure below.

Go back to previous section -- Go to next section

last updated: January 8, 2013

Author of original content: Nick Strobel