A satellite has a mass of 5850 kg and is in a circular orbit 3.8 105 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 106 m. What is the true weight of the satellite when it is at rest on the planet's surface?
My guess is about .025kg.
i did GM5850/4.15E6^2= 5850*217183.3^2/ 4.15E6
my V was 217183.3 then when i solved for GM i got 1.9574E37 and pluged that into the weight equation and it was marked wrong. someone please help
i did the same thing david did and gor the wrong answer please help me
To find the true weight of the satellite when it is at rest on the planet's surface, we need to first calculate the gravitational force acting on the satellite at its orbit, and then adjust it for the surface of the planet.
Step 1: Calculate the gravitational force acting on the satellite at its orbit.
The gravitational force acting on the satellite can be found using the formula:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67 × 10^-11 N m^2/kg^2), m1 is the mass of the satellite, m2 is the mass of the planet, and r is the distance between the center of the satellite and the center of the planet.
Given:
Mass of the satellite (m1) = 5850 kg
Radius of the planet (r) = 4.15 × 10^6 m
We need to determine the mass of the planet (m2). Unfortunately, the given information does not provide the mass of the planet. Therefore, we cannot calculate the exact gravitational force acting on the satellite.
However, we can still calculate the relative weight of the satellite compared to its weight at the surface of the planet, which is what we are asked for.
Step 2: Calculate the relative weight of the satellite.
The relative weight of the satellite is given by the equation:
Relative weight = (gravitational force at the orbit) / (gravitational force at the surface)
We need to calculate the gravitational force at the surface of the planet to find the relative weight. The gravitational force at the surface can be found using the formula:
F_surface = (G * m1 * m2) / r_surface^2
where F_surface is the gravitational force at the surface, r_surface is the radius of the planet.
Given:
Radius of the planet (r_surface) = 4.15 × 10^6 m
Now we can calculate the relative weight:
Relative weight = (gravitational force at the orbit) / (gravitational force at the surface)
Remember that we can't find the exact gravitational force on the satellite without knowing the mass of the planet, but we can still calculate the ratio of the forces.
GMm/d^2=mv^2/d where d is the orbital radius. v= 2PId/period, change the period to seconds, solve for v. Now,putting that into the equation, solve for GM
Then put GM in to the weight equation.
Weight=GM m/4.15E6^2