Given that the Earth's radius is 6.37x10^6 m and taking the earth's gravitational field at its surface to be 9.81N/kg, find the gravitational potential at the Earth's surface.
V=G*massearth/r
Where G*Massearth/r^2=9.81N/kg so
G*Massearth/r * r=9.81N/kg
So V= 9.81/r if r is in meters.
watch the units.
To find the gravitational potential at the Earth's surface, we can use the formula:
Gravitational Potential (V) = Gravitational Field Strength (g) * Height (h)
In this case, the height (h) is the distance from the Earth's surface to the center, which is equal to the Earth's radius (r).
Given:
Earth's radius (r) = 6.37x10^6 m
Gravitational field strength (g) = 9.81 N/kg
Now we can substitute the values into the formula:
V = g * h
V = 9.81 N/kg * 6.37x10^6 m
Calculating this:
V = 6.37x10^7 Nm/kg
So, the gravitational potential at the Earth's surface is 6.37x10^7 Nm/kg.
To find the gravitational potential at the Earth's surface, we can use the formula:
Gravitational Potential = Gravitational Field Strength * Height
In this case, the given height is the radius of the Earth which is 6.37x10^6 m, and the gravitational field strength at the Earth's surface is 9.81 N/kg. Plugging the values into the formula, we get:
Gravitational Potential = 9.81 N/kg * 6.37x10^6 m
Calculating this expression gives us the answer to the question.