Gradient: the change of a value (here: gravitational force, or rather: potential) over a reference variable (here e.g. the length of the body)
No, the absolute value of the gravitational force does not matter for the gradient. Gravitational force (potential) is proportional to the inverse distance squared from the center of mass that exerts the gravitational potential. If your distance from the object R is large enough, then the gradient of gravity across the length of your body is negligible:
In the worst case, with your body length being s, the gravity at the part of your body closest to the center of mass pulling you would be: F_max = F_min * ( R^2 / (R-s)^2 ), and with s << R, this becomes F_min, the force at the part of your body furthest away from the mass pulling you in.
This becomes problematic when you get “too close” to the body in question - and where too close begins, depends indeed on the absolute force. But for each black hole, there’s a safe distance at which you could fall around it, assuming no other factors killing you (like intersteller particles, or an accretion disc)
Gradient: the change of a value (here: gravitational force, or rather: potential) over a reference variable (here e.g. the length of the body)
No, the absolute value of the gravitational force does not matter for the gradient. Gravitational force (potential) is proportional to the inverse distance squared from the center of mass that exerts the gravitational potential. If your distance from the object R is large enough, then the gradient of gravity across the length of your body is negligible: In the worst case, with your body length being s, the gravity at the part of your body closest to the center of mass pulling you would be: F_max = F_min * ( R^2 / (R-s)^2 ), and with s << R, this becomes F_min, the force at the part of your body furthest away from the mass pulling you in.
This becomes problematic when you get “too close” to the body in question - and where too close begins, depends indeed on the absolute force. But for each black hole, there’s a safe distance at which you could fall around it, assuming no other factors killing you (like intersteller particles, or an accretion disc)
Makes sense, thank you :)