Question

a satellite is orbiting Earth at a distance of 35 kilometers. The satellite has a mass of 500 kilograms. what is the force between the planet and the satellite

Answer 1

Answer: F = 4.76 * 10³ N

Step-by-step explanation:

We know that the force of gravity between two objects is:

F = G*m*M/r²

Where M is the mass of earth, m is the mass of the satelite, r is the distance between the radius of the earth and the satelite and G is the gravitational constant, and the data that we have is:

Mass of satellite: m = 500 kg

Distance of the satellite from Earth's surface: H = 0.035x10^6 m

Radius of Earth: R = 6.4 x 10⁶ m

So we have that r = R + H = 6.435x10^6

Mass of Earth: M = 5.9 * 10²⁴ kg

Gravitational Constant: G = 6.673 x 10⁻¹¹ N m²/kg²

Then the force that the Earth does in the satellite is:

F = (1.97*10¹⁷)/(6.435*10⁶)²

F = (1.97*10¹⁷)/(4.14*10¹³)

F = 4.76 * 10³ N

Answer 2

The force between the planet and the satellite is 4.76 * 10³ Newtons

Step-by-step explanation:

Given:

Mass of satellite = m = 500 kg

Distance of the satellite from Earth's surface = h = 35000 m

We know that:

Mass of Earth = M = 5.9 * 10²⁴ kg

Radius of Earth = R = 6.4 * 10⁶ m

Gravitational Constant = G = 6.673 x 10⁻¹¹ N m²/kg²

Force between Earth and an object is given as:

F = GmM/(R+h)²

= (6.673 x 10⁻¹¹ x 500 x 5.9 x 10²⁴)/((6.4 * 10⁶)+(3.5*10⁴))²

= (1.97*10¹⁷)/(6.435*10⁶)²

= (1.97*10¹⁷)/(4.14*10¹³)

= 4.76 * 10³ N