The escape speed from a planet of mass 2.5×10^24 is 7.0 km/s.What is the planet's radius?
Iam using the formula v=sqr(2GM/r)
v=7
G=6.67*10^-11
M=2.5*10^24
r=?
I get 6.8*10^12
Where did I go wrong?
To find the radius of the planet using the formula v = sqrt(2GM/r), we can rearrange the equation to solve for r.
The equation becomes:
r = (2GM) / v^2
Let's substitute the given values:
G = 6.67 × 10^-11 m^3/kg/s^2
M = 2.5 × 10^24 kg
v = 7.0 km/s = 7.0 × 10^3 m/s
Now, we can calculate the radius:
r = (2 × 6.67 × 10^-11 × 2.5 × 10^24) / (7.0 × 10^3)^2
r = (13.34 × 10^13 × 10^24) / (49 × 10^6)
r = 13.34 × (10^13+24-6) / 49
r = 13.34 × 10^31 / 49
Now, divide 13.34 by 49:
r = 2.720×10^30
Therefore, the radius of the planet is approximately 2.720 × 10^30 meters.
It seems like there was a calculation error in your computation.