# What is the apparent weight of a 2000 kg satellite in a geosynchronous orbit?

Communications satellites are positioned in a round orbit the place they keep immediately over a hard and fast level on the equator because the earth rotates. These are referred to as geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 * 10^{7} m( approx 22,000 miles)

The drive of gravity is:
F = G mearth msat / r^2

The gravitational acceleration on the satellite tv for pc is:
g = G mearth / r^2

Lookup Newton’s G and the mass of the earth. They provide the mass of the radius of the orbit and the mass of the satellite tv for pc. Plugnchug.

Poorcoco’s interpretation is legitimate. The issue would not state what reference body you might be in, so you might say your reference body is orbiting with the satellite tv for pc, so the centrifugal drive cancels gravity and the obvious weight is zero. I feel they imply so that you can work in an inertial body, although, and really do the calculation.

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by means of truth the satellite tv for pc television for laptop is given a mass, this might properly be an actual 2 physique venture, the orbital radius (r) of the satellite tv for pc television for laptop and midsection to midsection distance (d) are , certainly , distinctive (very very barely for that purpose). The 24 hour period refers again to the picture voltaic day that is bigger than 360 ° of rotation. The rotational price of the earth is calculated making use of the sidereal rotation time for 360 °, that is = 23.934 hours / 86,164 seconds, which supplies 7.2921 e-5 radians / sec. This mother or father should be matched by the satellite tv for pc television for laptop for synchronous operation. apart from, by means of truth the options could be so shut (by means of mass proportion) , you might cheat barely : neglect roughly in regards to the satellite tv for pc television for laptop mass initially (which means r and d are =), you will have the orbital radius (r) (2.01 e8 meters) and the sidereal period (t) = 24 hours (86,4 hundred seconds), so paintings out the orbital velocity (v) after which the centripetal acceleration (a). v = (2 * pi * r ) / t = 14,617.13 m/s a = v ² / r = a million.063 m/s/s For steady orbit the gravitational acceleration (g) = a Now introduce the traditional equation : (m1 = planet mass, m2 = satellite tv for pc television for laptop mass) g = ( G * ( m1 + m2 ) ) / d ² you understand G, g, m2 = 0 and d = r , then transpose to operate m1 : m1 = ( g * r ² ) / G m1 = 6.4361 e26 kg ( reply b) ) Now the stress on all the 2 tons of from the traditional : f = ( G * m1 * m2 ) / d ² f = 617.fifty 9 Newtons ( reply a) )

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It is in orbit, so it is in freefall; its obvious weight is by definition zero. The gravitational acceleration is exactly equal to the centripetal acceleration.