A satellite has an orbit with pedigree 175 km and apogee 181,200 km. What is the period of the orbit?
>>I'm not sure what the associated equation is. I tried the problem using the average radius in the period equation but it didn't work. Please help!
First of all, the word is perigee, not pedigree. Pedigrees are used to breed animals.
The numbers you gave must be altitudes, not distances from the center of the Earth. Otherwise, the satellite would come crashing to the surface of the Earth.
Add the radius of the Earth to each. I believe that is something like 6376 km, on the average. That makes the distances from the ceneter of the Earth
6551 km for perigee and 187,576 for the apogee. The average of those two distances is called the semimajor axis of the elliptical orbit, and that is what determines the period. In this case, it is 97064 km.
Assuming it is an Earth satellite, use Kepler's third law (or wht you called the "period equation") to get the period. Since the apogee is nearly half way to the Moon, it is likely that this orbit would be highly perturbed.
To find the period of an orbit, we can use Kepler's Third Law, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis (a) of the orbit.
In this case, we are given the apogee (the point in the orbit farthest from Earth's center) and the perigee (the point in the orbit closest to Earth's center). The sum of the perigee and apogee distances is twice the semi-major axis (a).
Given that the perigee distance (rp) is 175 km and the apogee distance (ra) is 181,200 km, we can calculate the semi-major axis (a):
a = (rp + ra) / 2
= (175 km + 181,200 km) / 2
= 90,187.5 km
Now, we can use Kepler's Third Law to find the period (T):
T^2 = k * a^3
where k is a constant.
Since we want the period in seconds, let's convert the semi-major axis from kilometers to meters:
a = 90,187.5 km * (1000 m / 1 km)
= 90,187,500 m
Plugging in the values:
T^2 = k * (90,187,500 m)^3
We can solve for the period (T) by taking the square root of both sides:
T = sqrt(k * (90,187,500 m)^3)
Since we are given neither the gravitational constant (k) nor the units for T, we cannot calculate the exact value of T. However, this equation allows us to determine the relationship between the period and the semi-major axis.
To find the numerical value of the period, you would need either the gravitational constant (k) or an additional piece of information, such as the mass of the central body.