A 540 kg satellite orbits at a distance from the Earth's center of about 5.4 Earth radii. What gravitational force does the Earth exert on the satellite

1/5.4^2 * g

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To calculate the gravitational force that the Earth exerts on the satellite, we can use the formula for gravitational force:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (which is approximately 6.67430 × 10^-11 N(m/kg)^2),
m1 is the mass of the Earth (approximately 5.972 × 10^24 kg),
m2 is the mass of the satellite (540 kg),
and r is the distance between the center of the Earth and the satellite (5.4 Earth radii).

First, let's convert the distance to meters:

Distance = 5.4 Earth radii * radius of the Earth
= 5.4 * 6,371 km
= 34,434.6 km

Now, let's convert the distance to meters:

Distance in meters = 34,434.6 km * 1,000 m/km
= 34,434,600 m

Now we can calculate the gravitational force:

F = (6.67430 × 10^-11 N(m/kg)^2) * ((5.972 × 10^24 kg) * (540 kg)) / (34,434,600 m)^2

Simplifying the equation:

F = (6.67430 × 10^-11 N(m/kg)^2) * (3.22728 × 10^27 kg) / (1.18594 × 10^15 m^2)

Calculating the value:

F = 3.4049 × 10^17 N

Therefore, the gravitational force that the Earth exerts on the satellite is approximately 3.4049 × 10^17 N.

To calculate the gravitational force exerted by the Earth on the satellite, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula for gravitational force (F) is given by:

F = (G * m1 * m2) / r^2

Where:
F = gravitational force
G = gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 = mass of the first object (in this case, the Earth)
m2 = mass of the second object (in this case, the satellite)
r = distance between the centers of the two objects

In this case, the satellite's mass is given as 540 kg, and it orbits at a distance from the Earth's center of about 5.4 Earth radii. To calculate the actual distance between the two objects, we need to multiply the Earth radius (assumed to be constant) by the given distance.

Let's proceed with the calculations:

Earth radius = R
Distance between the objects (r) = 5.4 * R

Now, we can substitute the values into the equation and solve for the gravitational force (F):

F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * m1 * m2) / (5.4 * R)^2
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * mass of the Earth * 540 kg) / (5.4 * R)^2

To find the value for the mass of the Earth, we can use the standard value which is approximately 5.972 × 10^24 kg. Substitute this value, and you will have the exact gravitational force exerted by the Earth on the satellite.