A communications satellite with a mass of 450 kg is in a circular orbit about the Earth. The radius of the orbit is 2.9×10^4 km as measured from the center of the Earth.
Calculate the weight of the satellite on the surface of the Earth
Calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.
weight on Earth: mass*g
forceinorbit= g*mass*(re/(rorbit))^2
To calculate the weight of the satellite on the surface of the Earth, we can use the formula:
Weight = mass x gravitational acceleration
The gravitational acceleration on the surface of the Earth is approximately 9.8 m/s^2. However, since the mass is given in kilograms and the radius of the orbit is given in kilometers, we need to convert them to the appropriate units.
Mass of the satellite = 450 kg
Radius of the orbit = 2.9 x 10^4 km = 2.9 x 10^7 m
Converting the radius of the orbit from kilometers to meters:
Radius of the orbit = 2.9 x 10^7 m
Using the formula for weight:
Weight = mass x gravitational acceleration
= 450 kg x 9.8 m/s^2
= 4410 N
Therefore, the weight of the satellite on the surface of the Earth is 4410 Newtons.
To calculate the gravitational force exerted on the satellite by the Earth when it is in orbit, we can use the formula for gravitational force:
Gravitational force = (Gravitational constant x Mass of the satellite x Mass of the Earth) / (Radius of the orbit)^2
The gravitational constant is approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2.
Mass of the satellite = 450 kg
Mass of the Earth = 5.972 x 10^24 kg
Radius of the orbit = 2.9 x 10^7 m
Using the formula for gravitational force:
Gravitational force = (6.67430 x 10^-11 m^3 kg^-1 s^-2 x 450 kg x 5.972 x 10^24 kg) / (2.9 x 10^7 m)^2
≈ 2.68 x 10^5 N
Therefore, the gravitational force exerted on the satellite by the Earth when it is in orbit is approximately 2.68 x 10^5 Newtons.
To calculate the weight of the satellite on the surface of the Earth, you need to use the formula for weight:
Weight = mass × acceleration due to gravity
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s^2.
First, we need to convert the mass of the satellite from kilograms to grams, since the standard unit for weight is usually in grams.
1 kilogram = 1000 grams
Therefore, the mass of the satellite is 450 kg × 1000 g/kg = 450,000 grams.
Now, we can calculate the weight of the satellite on the surface of the Earth:
Weight = 450,000 g × 9.8 m/s^2 = 4,410,000 g·m/s^2
The weight of the satellite on the surface of the Earth is 4,410,000 grams-meters per second squared (g·m/s^2).
Now, let's calculate the gravitational force exerted on the satellite by the Earth when it is in orbit.
The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
Gravitational force = (Gravitational constant × mass of object 1 × mass of object 2) / distance^2
The mass of the Earth is approximately 5.97 × 10^24 kg.
The gravitational constant, G, is approximately 6.67430 × 10^-11 N(m/kg)^2.
The distance between the center of the Earth and the satellite in the given circular orbit is 2.9 × 10^4 km, which we need to convert to meters:
1 km = 1000 meters
Therefore, the distance is 2.9 × 10^4 km × 1000 m/km = 2.9 × 10^7 meters.
Now, we can calculate the gravitational force exerted on the satellite by the Earth in orbit:
Gravitational force = (6.67430 × 10^-11 N(m/kg)^2 × 450 kg × 5.97 × 10^24 kg) / (2.9 × 10^7 meters)^2
Simplifying the expression gives:
Gravitational force = 1.09120 × 10^18 N
The gravitational force exerted on the satellite by the Earth when it is in orbit is approximately 1.09120 × 10^18 Newtons (N).