A satellite has a mass of 5600 kg and is in a circular orbit 3.70*10^5 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.20*10^6 m. What is the true weight of the satellite when it is at rest on the planet's surface?
Inorbit?
ForceGravity=centripetal force
GMm/(3.7E5+4.6E6)^2=mv^2/r
but v= 2PIr/T
= m 4PI^2*(4.6E6+3.7E5)/T
solve for GM
Now, with GM known,
weight at the surface= m*GM/(4.2E6)^2
where did you get 4.6*10^6?
To find the true weight of the satellite when it is at rest on the planet's surface, we need to first calculate the weight of the satellite at its current position in the circular orbit, and then adjust it based on the gravitational force due to the planet.
1. Calculate the weight of the satellite in its current position:
The weight of the satellite in a circular orbit can be calculated using the formula: weight = mass × gravitational acceleration.
The mass of the satellite is given as 5600 kg.
The gravitational acceleration can be calculated using the formula: gravitational acceleration = G × mass of the planet / (radius of the planet + altitude of the satellite)^2.
The value of the gravitational constant G is 6.67430 × 10^-11 N*m^2/kg^2.
The radius of the planet is given as 4.20 × 10^6 m, and the altitude of the satellite is given as 3.70 × 10^5 m.
Weight of the satellite = mass × gravitational acceleration
2. Calculate the gravitational acceleration:
Substituting the given values, we have:
gravitational acceleration = (6.67430 × 10^-11 N*m^2/kg^2) × (mass of the planet) / (radius of the planet + altitude of the satellite)^2
3. Calculate the mass of the planet:
The mass of the planet is not given in the question. We need this information to calculate the gravitational acceleration. If you have the mass of the planet, substitute it into the formula.
4. Calculate the weight of the satellite:
With the gravitational acceleration calculated, we can now find the weight of the satellite in its current position using the formula: weight = mass × gravitational acceleration.
5. Adjust the weight to find the true weight on the planet's surface:
The true weight of the satellite on the planet's surface is the weight of the satellite in its current position minus the gravitational force due to the planet. This can be calculated using the formula: true weight = weight - mass × gravitational acceleration.
If you provide the mass of the planet, I can help you calculate the true weight of the satellite on the planet's surface.