(a) Calculate the magnitude of the gravitational force exerted on a 488-kg satellite that is a distance of 1.95 times earth radii from the center of the earth.
(b) What is the magnitude of the gravitational force exerted on the earth by the satellite?
(c) Determine the magnitude of the satellite's acceleration.
(d) What is the magnitude of the earth's acceleration?
(a) F =G•m •M/R²
the gravitational constant G =6.67•10^-11 N•m²/kg²,
Earth’s mass is M = 5.97•10^24 kg,
Earth’s radius is R = 6.378•10^6 m.
F =6.67•10^-11•488 • 5.97•10^24 /(1.5•6.378•10^6)²=…
(b) F =6.67•10^-11•488 • 5.97•10^24 /(1.5•6.378•10^6)²=…
(c) a1= F/m
(d) a2= F/M
To calculate the magnitude of the gravitational force, the equation for gravitational force can be used:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force
G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of the two objects (in this case, the satellite and the Earth)
r is the distance between the centers of the two objects
(a) For the satellite:
m1 = mass of the satellite = 488 kg
m2 = mass of the Earth = 5.972 x 10^24 kg (standard Earth mass)
r = distance = 1.95 times Earth radii = 1.95 * 6,371 km
First, convert the distance to meters:
r = 1.95 * 6,371 km * 1000 m/km = 12,493,550 m
Now, substitute the values into the equation and calculate the result:
F = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 488 kg * 5.972 x 10^24 kg) / (12,493,550 m)^2
Simplifying this equation will give you the magnitude of the gravitational force exerted on the satellite.
(b) To find the magnitude of the gravitational force exerted on the Earth by the satellite, the values for m1 and m2 need to be switched:
m1 = mass of the Earth = 5.972 x 10^24 kg
m2 = mass of the satellite = 488 kg
Now, substitute the values into the equation and calculate the result.
(c) To determine the magnitude of the satellite's acceleration, Newton's second law can be used:
F = m * a
where:
F is the gravitational force (calculated in part (a))
m is the mass of the satellite (488 kg)
a is the acceleration of the satellite
Rearranging the equation gives:
a = F / m
Substitute the values for F and m from part (a) into the equation and calculate the result.
(d) The magnitude of the Earth's acceleration due to the satellite can be calculated using Newton's second law:
F = m * a
where:
F is the gravitational force (calculated in part (b))
m is the mass of the Earth (5.972 x 10^24 kg)
a is the acceleration of the Earth
Rearranging the equation:
a = F / m
Substitute the values for F and m from part (b) into the equation and calculate the result.