How Close Can You Get to a Pulsar Without Being Torn Apart?

[dendiego]

A pulsar – a highly magnetized, rotating neutron star – has a radius of 9.98 Km, a mass of 1.98 × 1030 kg, and revolves around itself at a rate of 30.02 times per second. Calculate the nearest distance that a person 1.99 m tall could approach the pulsar without being pulled and torn apart. Assume that the mass of the person is uniform through out his/her body and the feet point toward the pulsar, and dismemberment starts when the force that each half of his/her body exerts on the other exceeds ten times his/her body weight on our planet earth. Also calculate the period of revolution that the body will cover in a circular orbit about the pulsar at this minimum distance.

what am I suppose to begin I have tried using the basic gravitation equation but my teacher said we will need a Taylor series to solve but i don't know how that relates ?
my best guess is that it is used to find the actual distance correct?

 

[cepheid]

Welcome to PF!

Up until now, with Newton's law of gravitation, you've always assumed objects are point masses i.e. all of the mass of that object is concentrated at one point in space (the centre of that object). This is reasonable if the masses are far away from each other, relative to their size. However, a feature of a neutron star is that it is very compact (dense), meaning at a LOT of mass (the mass of an entire sun) is crammed into a very small volume (10 km, the size of a city). This means that you can get very close to this object, which means that you can experience very very VERY strong gravity due to it. In particular, the point mass approximation is no longer the whole story. You have to consider tidal effects. Your feet are closer to the neutron star than your head. Newton's law of gravitation says that the strength of the gravitational force depends inversely on the square of the distance. Since your feet are closer than your head, your feet experience a stronger gravitational pull than your head, and your body gets stretched. These stretching forces are called tidal forces. They are responsible for the tides on Earth, for example. This problem is asking how close you can get before you get torn apart by tidal forces, where a criterion for being "torn apart' is given in the problem (when the acceleration corresponding to the tidal force exceeds 10g). So, you have to use Newton's Law of Gravitation to figure out the difference between the force on your feet and on your head, and therefore the force of stretching. Yes, a Taylor series expansion may be useful here. Do you know what a Taylor series is?