The MASS OF A SATELLITE IS 2000Kg .DETERMINE THE WEIGHT OF OF THE THE SATELLITE WHEN IT IS

(i)resting on the earth
(ii) 1000km above earth surface

Weight is equal to the mass of the object multiplied by the force of gravity attracting the object. giving the equation W=mg with mass in kg

(i)W=2000x9.8
= 19,600N

(ii) for this one we need to work out what the force of gravity will be at an altitude of 1000km above the Earth's surface
the equation to find g = GM/r^2
where G is universal gravitational constant 6.67x10^-11
M is the mass of the central body (earth)
and r is the distance between the center of masses of the 2 objects in meters(earth and satellite) we will assume that it is 1000km to the center of the satellite.
so g = (6.67x10^-11 x 5.98x10^24)/(6.98x10^6 + 1x10^6)^2
g = 6.26 m/s^2
if working with an object at an altitude do not forget to factor in the radius of the central body to your "r" value. in this case it is the radius of the earth (6.98x10^6 m)
now we put the value calculated above back into the equation W=mg
so the weight of the satellite at an altitude of 1000km = approximately 12,527N

hope this helps :) feel free to ask for clarification, i know its not the clearest

The previous answer posted by Jordan uses a correct approach but the wrong radius for the Earth. The mean radius is 6.378*10^6 km, not 6.98x10^6 m.

This makes the answer to part (ii)
g'(1000 km) = g(sea level)*(6378/7378)^2
g' = 7.33 m/s^2

The satellite weight at 1000 km altitude is therefore 14,700 N, rounded to three significant figures.

To determine the weight of the satellite, we need to multiply its mass by the acceleration due to gravity, which is approximately 9.8 m/s^2 on the surface of the Earth.

(i) When the satellite is resting on the Earth's surface, it experiences the full effect of gravity. Therefore, the weight of the satellite can be calculated using the formula:

Weight = Mass x Acceleration due to gravity

Weight = 2000 kg x 9.8 m/s^2
Weight = 19,600 Newtons (N)

Therefore, the weight of the satellite when it is resting on the Earth is 19,600 Newtons.

(ii) When the satellite is 1000 km above the Earth's surface, the distance between the satellite and the center of the Earth increases. At this height, the acceleration due to gravity is slightly lower than on the Earth's surface. To calculate the weight, we need to use the inverse square law:

Weight = Mass x (Acceleration due to gravity / (1 + (height of satellite / radius of Earth))^2)

The radius of the Earth is approximately 6371 km (6,371,000 meters). Converting the distance from km to meters, we have:

Height of satellite = 1000 km = 1,000,000 meters

Now, let's plug in the values into the formula:

Weight = 2000 kg x (9.8 m/s^2 / (1 + (1,000,000 m / 6,371,000 m))^2)

Calculating this expression:

Weight ≈ 2000 kg x (9.8 m/s^2 / 1.1569)^2
Weight ≈ 2000 kg x (8.493 m/s^2)^2
Weight ≈ 2000 kg x 72.043 m/s^2
Weight ≈ 144,086 Newtons (N)

Therefore, the weight of the satellite when it is 1000 km above the Earth's surface is approximately 144,086 Newtons.