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The value of $\gamma$ that I will use is

$\gamma=\sqrt(1-\frac{v^2}{c^2})$

And length contraction is

$L_0=\frac{L}{\gamma}$

Where all variables have usual meaning.

Let the gravitational pull on Mercury due to Sun be

$F=G\frac{M_s M_m}{r^2}$

Based on above formula, if we calculate precession of the perihelion of Mercury, the value is less by about 43 seconds of arc per century. That missing value comes from relativity effects.

My thinking is that the Newtonian gravity formula underestimates the value of Gravitational force of Sun on Mercury and that is why the precession of the perihelion is less.

So, I try to substitute length contraction formula in Newtonian gravity to "somehow account for relativity effects" i.e.

$F=G\frac{M_s M_m \gamma^2}{r^2}$

But since $\gamma \leq 1$ for $v\leq c$, the modified Newtonian gravity formula gives reduced value of gravitational force of Sun on Mercury.

So, my question is:

1. Is the gravitational force of Sun on Mercury due to relativistic effect less than the value obtained from Newton formula?

2. How to properly substitute length contraction in Newton formula?

The value of $\gamma$ that I will use is

$$\gamma=\sqrt{1-\frac{v^2}{c^2}}$$

And length contraction is

$$L_0=\frac{L}{\gamma}$$

Where all variables have usual meaning.

Let the gravitational pull on Mercury due to Sun be

$$F=G\frac{M_s M_m}{r^2}$$

Based on above formula, if we calculate precession of the perihelion of Mercury, the value is less by about 43 seconds of arc per century. That missing value comes from relativity effects.

My thinking is that the Newtonian gravity formula underestimates the value of Gravitational force of Sun on Mercury and that is why the precession of the perihelion is less.

So, I try to substitute length contraction formula in Newtonian gravity to "somehow account for relativity effects" i.e.

$$F=G\frac{M_s M_m \gamma^2}{r^2}$$

But since $\gamma \leq 1$ for $v\leq c$, the modified Newtonian gravity formula gives reduced value of gravitational force of Sun on Mercury.

So, my question is:

1. Is the gravitational force of Sun on Mercury due to relativistic effect less than the value obtained from Newton formula?

2. How to properly substitute length contraction in Newton formula?

The value of $\gamma$ that I will use is

$\gamma=\sqrt(1-\frac{v^2}{c^2})$

And length contraction is

$L_0=\frac{L}{\gamma}$

Where all variables have usual meaning.

Let the gravitational pull on Mercury due to Sun be

$F=G\frac{M_s M_m}{r^2}$

Based on above formula, if we calculate precession of the perihelion of Mercury, the value is less by about 43 seconds of arc per century. That missing value comes from relativity effects.

My thinking is that the Newtonian gravity formula underestimates the value of Gravitational force of Sun on Mercury and that is why the precession of the perihelion is less.

So, I try to substitute length contraction formula in Newtonian gravity to "somehow account for relativity effects" i.e.

$F=G\frac{M_s M_m \gamma^2}{r^2}$

But since $\gamma \leq 1$ for $v\leq c$, the modified Newtonian gravity formula gives reduced value of gravitational force of Sun on Mars.

So, my question is:

1. Is the gravitational force of Sun on Mars due to relativistic effect less than the value obtained from Newton formula?

2. How to properly substitute length contraction in Newton formula?

The value of $\gamma$ that I will use is

$\gamma=\sqrt(1-\frac{v^2}{c^2})$

And length contraction is

$L_0=\frac{L}{\gamma}$

Where all variables have usual meaning.

Let the gravitational pull on Mercury due to Sun be

$F=G\frac{M_s M_m}{r^2}$

Based on above formula, if we calculate precession of the perihelion of Mercury, the value is less by about 43 seconds of arc per century. That missing value comes from relativity effects.

My thinking is that the Newtonian gravity formula underestimates the value of Gravitational force of Sun on Mercury and that is why the precession of the perihelion is less.

So, I try to substitute length contraction formula in Newtonian gravity to "somehow account for relativity effects" i.e.

$F=G\frac{M_s M_m \gamma^2}{r^2}$

But since $\gamma \leq 1$ for $v\leq c$, the modified Newtonian gravity formula gives reduced value of gravitational force of Sun on Mercury.

So, my question is:

1. Is the gravitational force of Sun on Mercury due to relativistic effect less than the value obtained from Newton formula?

2. How to properly substitute length contraction in Newton formula?