Posted by Michael on January 01, 2000 at 23:34:00:
In Reply to: Re: What keeps Hubble up posted by Arlie on December 25, 1999 at 21:01:33:
> > Hubble, and all "things" in orbit, are actually continuously falling towards the earth due to gravity. However, the velocity (or speed) of the "thing" in orbit is such that it always remains at a relatively constant distance above earth.
The velocity of an object in orbit is given by the following formula:
v = (GM/r)^0.5, where
v is the velocity of the object in orbit, in metres per second (m/s)
G is the Universal Gravitaional constant equal to 6.67 x 10^-11 Nm^2/kg^2
M is the mass of the earth equal to 5.98 x 10^24 kg
r is the distance between Hubble's centre of mass and the earth's.
Hubble is 590 km above the surface of the earth at sea level and the radius of the earth is 6370 km. So r for Hubble is 6960 km or 6 960 000 m.
Hubble is not in airless space, so as it moves around the earth, there is some drag on it, which causes its orbit to decay slightly. But, if there was no drag on it, its orbit would be maintained forever. An object is maintained in orbit by its weight providing the necessary centripetal force. Hubble's weight is calculated by the formula which relates the force of attraction between two masses:
F = GMm/r^2, where
F is the weight of the object, in this case Hubble in newtons (N)
m is the mass of hubble in kilograms equal to 11 300 kg
the rest of the constants are as defined above.
Plugging in the numbers, Hubbles weight is about 93 kN. If one divides Hubble's weight by Hubble's mass, one can calculate the value of "g" where hubble is, and that is 8.23 m/s^2. If one divides 8.23 m/s^2 by 9.806 65 m/s^2, the standard value for "g" at sea level, one gets 0.84, or 84 %.
Astronauts/Cosmonauts are not really weightless on Hubble. Their weight gives them the centripetal force to fall around the earth at the same velocity Hubble is. They appear weightless, because they are not being attracted to Hubble by Hubble's mass. Objects in a skyscaper on earth might appear to be attracted to the floor of the building, but in reality they are being attracted to the earth's centre. But, the floor gets in the way and offers a resistance to the force due to gravity that is pulling on the objects, just like the earth's surface resists objects trying passing through it to get to the centre.