a planet has a radius of 5950 km and a value of g at the surface of 8 m/s2. If the planet decides to put a satellite into citcular orbit, what horizontal (orbital) speed must the satellite achieve?
To find the orbital speed of a satellite, we can use the formula:
v = √(g * r)
Where:
v is the orbital speed
g is the acceleration due to gravity at the surface of the planet
r is the radius of the planet
In this case, the values given are:
g = 8 m/s^2 (acceleration due to gravity)
r = 5950 km = 5950 * 1000 m (radius)
Let's calculate it step by step:
1. Convert the radius from kilometers to meters:
r = 5950 km * 1000 m/km
r = 5,950,000 m
2. Substitute the values in the formula:
v = √(8 m/s^2 * 5,950,000 m)
v ≈ √(47,600,000 m^2/s^2)
v ≈ 6,900 m/s
Therefore, the satellite must achieve an orbital speed of approximately 6,900 m/s.