How far from Saturn must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Saturn's pull?
I have the following values:
-distance between the Sun and Saturn: 1430e6
-mass of Sun: 1.99e30
-mass of Saturn: 5.69e26
-distance of probe: d (variable)
I used the ratio [(MASS sun)/(MASS saturn)]=[(d^2)/((distance between sun and saturn)-y)^2)]
The answer I got was 715,000,000 km, however it was wrong. Does anyone know the correct way to handle this problem? Thank you.
I have the following values:
-distance between the Sun and Saturn: 1430e6
-mass of Sun: 1.99e30
-mass of Saturn: 5.69e26
-distance of probe: d (variable)
I used the ratio [(MASS sun)/(MASS saturn)]=[(d^2)/((distance between sun and saturn)-y)^2)]
The answer I got was 715,000,000 km, however it was wrong. Does anyone know the correct way to handle this problem? Thank you.
-
I get 23,778,439 km. That's the point where
M[sun] / (1430e6 - d)^2 = M[saturn] / d^2
M[sun] / (1430e6 - d)^2 = M[saturn] / d^2
-
1.99e30 x d^2 = 5.69e26 x (1430e6-d)^2
1.99e30/5.69e26 = (1430e6-d)^2 / d^2
Since the number on the left is nearly 3500,
the "-d" on the right can be nearly ignored, so
3497 = (1430e6/d)^2
d = 1430e6/sqrt(3497) = about 409,000 km from Saturn
1.99e30/5.69e26 = (1430e6-d)^2 / d^2
Since the number on the left is nearly 3500,
the "-d" on the right can be nearly ignored, so
3497 = (1430e6/d)^2
d = 1430e6/sqrt(3497) = about 409,000 km from Saturn