To calculate the gravitational force intensity due to the Earth, we can use the formula:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the object, and r is the distance between the centers of the Earth and the object.
Given: Mass of the Earth (m1) = 5.78 x 10^24 kg Gravitational constant (G) = 6.67 x 10^-11 N m^2/kg^2 Radius of the Earth (r) = 6400 km = 6,400,000 m
Now, let’s calculate the gravitational force intensity due to the Earth:
F = (G * m1) / r^2
F = (6.67 x 10^-11 N m^2/kg^2 * 5.78 x 10^24 kg) / (6,400,000 m)^2
F = (3.8766 x 10^14 N m^2/kg^2) / (40,960,000,000 m^2)
F ≈ 9.48 x 10^3 N/kg
The gravitational force intensity due to the Earth is approximately 9.48 x 10^3 N/kg.
To calculate the escape velocity, we can use the formula:
v = √(2 * G * m1 / r)
where v is the escape velocity.
Now, let’s calculate the escape velocity:
v = √(2 * G * m1 / r)
v = √(2 * 6.67 x 10^-11 N m^2/kg^2 * 5.78 x 10^24 kg / 6,400,000 m)
v ≈ √(9.17 x 10^14 N m^2/kg^2 / 6,400,000 m)
v ≈ √(1.432 x 10^8 N m^2/kg^2)
v ≈ 1.195 x 10^4 m/s
The escape velocity from the Earth is approximately 1.195 x 10^4 m/s.

To calculate the gravitational force intensity due to the Earth, you can use the formula:
 
F = (G * m1 * m2) / r^2
 
where:
F is the gravitational force intensity,
G is the gravitational constant (6.67 * 10^-11 N(m/kg)^2),
m1 is the mass of the Earth (5.78 * 10^24 kg),
m2 is the mass of an object (assuming it is much smaller than the Earth’s mass, we can consider it negligible),
and r is the radius of the Earth (6400 km or 6.4 * 10^6 m).
 
Substituting the values into the formula:
 
F = (6.67 * 10^-11 N(m/kg)^2 * 5.78 * 10^24 kg * m2) / (6.4 * 10^6 m)^2
 
F = (4.44906 * 10^14 N * m2) / 4.096 * 10^13 m^2
 
F ≈ 10.88 N * m2 / m^2
 
The gravitational force intensity due to the Earth is approximately 10.88 N.
 
Now, to calculate the escape velocity, we can use the formula:
 
v = √(2 * G * M / r)
 
where:
v is the escape velocity,
G is the gravitational constant (6.67 * 10^-11 N(m/kg)^2),
M is the mass of the Earth (5.78 * 10^24 kg),
and r is the radius of the Earth (6400 km or 6.4 * 10^6 m).
 
Substituting the values into the formula:
 
v = √(2 * 6.67 * 10^-11 N(m/kg)^2 * 5.78 * 10^24 kg / 6.4 * 10^6 m)
 
v = √(7.53676 * 10^13 N * m / 4.096 * 10^6 m)
 
v ≈ √(18.3789 * 10^6 m^2/s^2)
 
v ≈ 4285.5 m/s
 
Therefore, the escape velocity from the Earth is approximately 4285.5 m/s.