If the diameter is d = 1600km, then the radius is r = 800 km, or 800,000 meters. The formula for the volume V of a sphere with radius r is:
. . . . .V = (4/3)(pi)(r^3)
Then the volume of the planet is:
. . . . .V = (4/3)(pi)(800^3 km^3)
. . . . .. .= (4/3)(pi)(800000^3 m^3)
. . . . .. .= (pi/3)(2.048?-10^18) m^3
With a density of 5200 kg/m^3, we get a total mass M of:
. . . . .M = (volume) ?- (mass/volume)
. . . .. . .= (pi/3)(2.048?-10^18 m^3) ?- (5200 kg/m^3)
. . . .. . .= (pi/3)(1.06496?-10^22) kg
...or about 1.1152235?-10^22 kilograms.
Since the satellite is 630 km = 630,000 meters above the surface, it is then 630 km + 800 km = 1430 km = 1,430,000 meters from the center of the planet. So R = 1,430,000 m. Taking the gravitational constant (which we will assume is the same in the Neopets' universe as in our own) as:
. . . . .G = (2/3)?-10^(-10)(m^3 / (kg s^2))
...and using the standard formula for orbital velocity v:
. . . . .v = sqrt[(GM)/R]
...we get:
. . . . .v = sqrt[(2/3)(10^(-10))(pi/3)(1.06596)(10^22) / 1,430,000] m/s
. . . .. . .= sqrt[520405.9215...] m/s (approx)
. . .. . . .= 721.3916561... m/s (approx)
Rounding UP, we get 722 meters per second.
Please check my work.
Eliz.
Answers.com: orbital velocity
Astronomy 106: Orbital Velocity