Find equation for mass in gravityA satellite is moving in circular motion round a planet.From the physics we know that Σ F r = m a r = G M m r 2 So I wanted to find the equation for M knowing also that v = ω r = 2 π r T and a r = v 2 r Thus, m a r = G M m r 2 a r = G M r 2 v 2 r = G M r 2 ( 2 π r T ) 2 r = G M r 2 4 π 2 r 2 T 2 r = G M r 2 4 π 2 r 3 T 2 = G M r 2 4 π 2 r 5 T 2 = G M 4 π 2 r 5 G T 2 = MHowever, this is wrong! It should be: M = 4 π 2 r 3 G T 2 What was my mistake in Mathematics? Please don't migrate it to physics because my misunderstanding is on math.Note: I would be very happy if you show my mistake, instead of showing me another way to get to the equation.

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Find equation for mass in gravityA satellite is moving in circular motion round a planet.From the physics we know that  Σ      F    r    =  m      a    r    =            G      M      m              r      2      So I wanted to find the equation for   M knowing also that  v  =  ω  r  =            2      π      r        T  and      a    r    =            v      2        r  Thus,  m      a    r    =            G      M      m              r      2            a    r    =            G      M              r      2                  v      2        r    =            G      M              r      2                          (                              2            π            r                    T                )            2        r    =            G      M              r      2                          4                  π          2                          r          2                            T        2              r    =            G      M              r      2                  4              π        2                    r        3                    T      2        =            G      M              r      2                  4              π        2                    r        5                    T      2        =  G  M            4              π        2                    r        5            G              T      2        =  MHowever, this is wrong! It should be:  M  =            4              π        2                    r        3                    G              T        2            What was my mistake in Mathematics? Please don&#039;t migrate it to physics because my misunderstanding is on math.Note: I would be very happy if you show my mistake, instead of showing me another way to get to the equation.

tennispopj8 · Accepted Answer

4              π        2                    r        2                    T      2            /    r  =            4      π      r              T      2       and G should go down not up in numerator.

polivijuye · Accepted Answer

The mistake lies in these steps:                    4                  π          2                          r          2                            T        2              r    =            G      M              r      2                  4              π        2                    r        3                    T      2        =            G      M              r      2                  4              π        2                    r        5                    T      2        =  G  M            4              π        2                    r        5            G              T      2        =  MActually, it should have been:                    4                  π          2                          r          2                            T        2              r    =            G      M              r      2                  4              π        2            r              T      2        =            G      M              r      2                  4              π        2                    r        3                    T      2        =  G  M            4              π        2                    r        3                    G              T        2              =  M1.In the second step, the numerator will have   r and not       r    3  2.In the last step,   G will be in the denominator.

Find equation for mass in gravity A satellite is moving in circular motion round a planet. From t

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