a satellite has a mass of 100 kg and is located at 2 x 10^6 m above the surface if the Earth. wHAT is the potential energy associated with the satellite at this location? What is the magnitude of the gravitational force on the satellite?
To calculate the potential energy associated with the satellite, we can use the formula:
Potential Energy = mass x acceleration due to gravity x height
Given that the mass of the satellite is 100 kg and the height above the surface of the Earth is 2 x 10^6 m, we need to find the acceleration due to gravity, which can be considered a constant value near the surface of the Earth and is approximately 9.8 m/s^2.
Calculating the potential energy:
Potential Energy = 100 kg x 9.8 m/s^2 x 2 x 10^6 m
= 1.96 x 10^9 J
Hence, the potential energy associated with the satellite at this location is 1.96 x 10^9 Joules.
To determine the magnitude of the gravitational force on the satellite, we can use the formula:
Gravitational Force = mass x acceleration due to gravity
Using the given mass of the satellite as 100 kg and the value of the acceleration due to gravity as 9.8 m/s^2:
Gravitational Force = 100 kg x 9.8 m/s^2
= 980 N
Thus, the magnitude of the gravitational force acting on the satellite is 980 Newtons.
To calculate the potential energy associated with the satellite, we can use the formula:
Potential Energy = mass x gravitational acceleration x height
Given:
Mass of the satellite (m) = 100 kg
Height from Earth's surface (h) = 2 x 10^6 m (2 million meters)
The gravitational acceleration (g) on Earth is approximately 9.8 m/s^2.
Plugging in the values into the formula:
Potential Energy = 100 kg x 9.8 m/s^2 x 2 x 10^6 m
Potential Energy = 100 kg x 9.8 m/s^2 x 2,000,000 m
Potential Energy = 1,960 x 10^6 J
Therefore, the potential energy associated with the satellite at this location is 1,960 x 10^6 Joules.
To calculate the magnitude of the gravitational force on the satellite, we can use the formula:
Gravitational Force = mass x gravitational acceleration
Plugging in the values:
Gravitational Force = 100 kg x 9.8 m/s^2
Gravitational Force = 980 N
Therefore, the magnitude of the gravitational force acting on the satellite is 980 Newtons.
The earth's radius is about Re = 6.4*10^6 m. At 2*10^6 m above the surface, you are R = 8.4*10^6 m from the center of the Earth. The acceleration of gravity is reduced by a ratio
(6.4/8.4)^2 = 0.58
and g is reduced to g'= 5.7 m/s^2
The potential energy (relative to the ground), is M G[1/Re - 1/R]. G is the universal constant here.
This P.E. will be somewhat less than
M * g *altitude, because g is not constant with altitude
The gravity force is M g'