A satellite moves in a circular orbit around Earth at a speed of 4390 m/s
(a) Determine the satellite's altitude above the surface of Earth.(meters)
(b) Determine the period of the satellite's orbit.
(hours)
I used the equation M(sattelite)V^2/r = M(sattelite)(Mass(earth)G/r^2
and tried to solve for r by canceling out one r and the M(sattelite) which gave me
r = GM(earth)/v^2
the answer i keep getting is 20,592,718.12m
but it is not right....
Have you tried subtracting the radius of the Earth? They asked for the altitude. "r" is the distance from the center of the Earth.
oh wow, thanks....
wish I would have thought of that.
it worked.
To solve this problem, you are on the right track using the equation M(satellite)V^2/r = M(satellite)(Mass(earth)G/r^2. However, you made a mistake in cancelling out the terms.
To determine the satellite's altitude above the surface of Earth, we can use the equation you mentioned:
M(satellite)V^2 / r = M(satellite)(Mass(earth)G / r^2
Where:
M(satellite) is the mass of the satellite
V is the velocity of the satellite
r is the radius of the orbit
Mass(earth) is the mass of the Earth
G is the gravitational constant
To solve for r, we can simply rearrange the equation:
r = (M(satellite)V^2) / (M(earth)G)
Now let's put in the known values:
M(satellite) can be assumed to be negligible compared to the mass of the Earth, so we can cancel it out.
V = 4390 m/s
M(earth) = 5.97 × 10^24 kg
G = 6.67 × 10^-11 Nm^2/kg^2
r = (V^2) / (M(earth)G)
r = (4390^2) / (5.97 × 10^24 * 6.67 × 10^-11)
Calculating this gives us:
r ≈ 2.99 × 10^7 meters
So the satellite's altitude above the surface of Earth is approximately 29,900,000 meters.
Now, to determine the period of the satellite's orbit, we can use the formula:
T = (2πr) / V
Where:
T is the period of the orbit in seconds
r is the radius of the orbit
V is the velocity of the satellite
Substituting in the known values:
T = (2π * 2.99 × 10^7) / 4390
Calculating this gives us:
T ≈ 4.07 × 10^4 seconds
To convert this into hours:
T(hours) = T(seconds) / 3600
Calculating this gives us:
T ≈ 11.3 hours
So the period of the satellite's orbit is approximately 11.3 hours.